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Simplifying (8x + 3)(8x + 1)(10x + 1) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: (3 + 8x)(8x + 1)(10x + 1) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: (3 + 8x)(1 + 8x)(10x + 1) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: (3 + 8x)(1 + 8x)(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Multiply (3 + 8x) * (1 + 8x) (3(1 + 8x) + 8x * (1 + 8x))(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) ((1 * 3 + 8x * 3) + 8x * (1 + 8x))(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) ((3 + 24x) + 8x * (1 + 8x))(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) (3 + 24x + (1 * 8x + 8x * 8x))(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) (3 + 24x + (8x + 64x2))(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 24x + 8x = 32x (3 + 32x + 64x2)(1 + 10x) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Multiply (3 + 32x + 64x2) * (1 + 10x) (3(1 + 10x) + 32x * (1 + 10x) + 64x2 * (1 + 10x)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) ((1 * 3 + 10x * 3) + 32x * (1 + 10x) + 64x2 * (1 + 10x)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) ((3 + 30x) + 32x * (1 + 10x) + 64x2 * (1 + 10x)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) (3 + 30x + (1 * 32x + 10x * 32x) + 64x2 * (1 + 10x)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) (3 + 30x + (32x + 320x2) + 64x2 * (1 + 10x)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) (3 + 30x + 32x + 320x2 + (1 * 64x2 + 10x * 64x2)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) (3 + 30x + 32x + 320x2 + (64x2 + 640x3)) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 30x + 32x = 62x (3 + 62x + 320x2 + 64x2 + 640x3) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 320x2 + 64x2 = 384x2 (3 + 62x + 384x2 + 640x3) + (8x + 4)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 62x + 384x2 + 640x3 + (4 + 8x)(6x + 1)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 62x + 384x2 + 640x3 + (4 + 8x)(1 + 6x)(10x + 1) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 62x + 384x2 + 640x3 + (4 + 8x)(1 + 6x)(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Multiply (4 + 8x) * (1 + 6x) 3 + 62x + 384x2 + 640x3 + (4(1 + 6x) + 8x * (1 + 6x))(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + ((1 * 4 + 6x * 4) + 8x * (1 + 6x))(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + ((4 + 24x) + 8x * (1 + 6x))(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + (4 + 24x + (1 * 8x + 6x * 8x))(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + (4 + 24x + (8x + 48x2))(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 24x + 8x = 32x 3 + 62x + 384x2 + 640x3 + (4 + 32x + 48x2)(1 + 10x) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Multiply (4 + 32x + 48x2) * (1 + 10x) 3 + 62x + 384x2 + 640x3 + (4(1 + 10x) + 32x * (1 + 10x) + 48x2 * (1 + 10x)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + ((1 * 4 + 10x * 4) + 32x * (1 + 10x) + 48x2 * (1 + 10x)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + ((4 + 40x) + 32x * (1 + 10x) + 48x2 * (1 + 10x)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + (4 + 40x + (1 * 32x + 10x * 32x) + 48x2 * (1 + 10x)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + (4 + 40x + (32x + 320x2) + 48x2 * (1 + 10x)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + (4 + 40x + 32x + 320x2 + (1 * 48x2 + 10x * 48x2)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + (4 + 40x + 32x + 320x2 + (48x2 + 480x3)) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 40x + 32x = 72x 3 + 62x + 384x2 + 640x3 + (4 + 72x + 320x2 + 48x2 + 480x3) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 320x2 + 48x2 = 368x2 3 + 62x + 384x2 + 640x3 + (4 + 72x + 368x2 + 480x3) + -1(8x + 5)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 8x)(6x + 1)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 8x)(1 + 6x)(8x + 1) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 8x)(1 + 6x)(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) Multiply (5 + 8x) * (1 + 6x) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5(1 + 6x) + 8x * (1 + 6x))(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1((1 * 5 + 6x * 5) + 8x * (1 + 6x))(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1((5 + 30x) + 8x * (1 + 6x))(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 30x + (1 * 8x + 6x * 8x))(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 30x + (8x + 48x2))(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 30x + 8x = 38x 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 38x + 48x2)(1 + 8x) = 2((6x + 1)(8x + 1)(10x + 1)) Multiply (5 + 38x + 48x2) * (1 + 8x) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5(1 + 8x) + 38x * (1 + 8x) + 48x2 * (1 + 8x)) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1((1 * 5 + 8x * 5) + 38x * (1 + 8x) + 48x2 * (1 + 8x)) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1((5 + 40x) + 38x * (1 + 8x) + 48x2 * (1 + 8x)) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 40x + (1 * 38x + 8x * 38x) + 48x2 * (1 + 8x)) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 40x + (38x + 304x2) + 48x2 * (1 + 8x)) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 40x + 38x + 304x2 + (1 * 48x2 + 8x * 48x2)) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 40x + 38x + 304x2 + (48x2 + 384x3)) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 40x + 38x = 78x 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 78x + 304x2 + 48x2 + 384x3) = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 304x2 + 48x2 = 352x2 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + -1(5 + 78x + 352x2 + 384x3) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + (5 * -1 + 78x * -1 + 352x2 * -1 + 384x3 * -1) = 2((6x + 1)(8x + 1)(10x + 1)) 3 + 62x + 384x2 + 640x3 + 4 + 72x + 368x2 + 480x3 + (-5 + -78x + -352x2 + -384x3) = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 3 + 4 + -5 + 62x + 72x + -78x + 384x2 + 368x2 + -352x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 3 + 4 = 7 7 + -5 + 62x + 72x + -78x + 384x2 + 368x2 + -352x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 7 + -5 = 2 2 + 62x + 72x + -78x + 384x2 + 368x2 + -352x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 62x + 72x = 134x 2 + 134x + -78x + 384x2 + 368x2 + -352x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 134x + -78x = 56x 2 + 56x + 384x2 + 368x2 + -352x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 384x2 + 368x2 = 752x2 2 + 56x + 752x2 + -352x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 752x2 + -352x2 = 400x2 2 + 56x + 400x2 + 640x3 + 480x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 640x3 + 480x3 = 1120x3 2 + 56x + 400x2 + 1120x3 + -384x3 = 2((6x + 1)(8x + 1)(10x + 1)) Combine like terms: 1120x3 + -384x3 = 736x3 2 + 56x + 400x2 + 736x3 = 2((6x + 1)(8x + 1)(10x + 1)) Reorder the terms: 2 + 56x + 400x2 + 736x3 = 2((1 + 6x)(8x + 1)(10x + 1)) Reorder the terms: 2 + 56x + 400x2 + 736x3 = 2((1 + 6x)(1 + 8x)(10x + 1)) Reorder the terms: 2 + 56x + 400x2 + 736x3 = 2((1 + 6x)(1 + 8x)(1 + 10x)) Multiply (1 + 6x) * (1 + 8x) 2 + 56x + 400x2 + 736x3 = 2((1(1 + 8x) + 6x * (1 + 8x))(1 + 10x)) 2 + 56x + 400x2 + 736x3 = 2(((1 * 1 + 8x * 1) + 6x * (1 + 8x))(1 + 10x)) 2 + 56x + 400x2 + 736x3 = 2(((1 + 8x) + 6x * (1 + 8x))(1 + 10x)) 2 + 56x + 400x2 + 736x3 = 2((1 + 8x + (1 * 6x + 8x * 6x))(1 + 10x)) 2 + 56x + 400x2 + 736x3 = 2((1 + 8x + (6x + 48x2))(1 + 10x)) Combine like terms: 8x + 6x = 14x 2 + 56x + 400x2 + 736x3 = 2((1 + 14x + 48x2)(1 + 10x)) Multiply (1 + 14x + 48x2) * (1 + 10x) 2 + 56x + 400x2 + 736x3 = 2((1(1 + 10x) + 14x * (1 + 10x) + 48x2 * (1 + 10x))) 2 + 56x + 400x2 + 736x3 = 2(((1 * 1 + 10x * 1) + 14x * (1 + 10x) + 48x2 * (1 + 10x))) 2 + 56x + 400x2 + 736x3 = 2(((1 + 10x) + 14x * (1 + 10x) + 48x2 * (1 + 10x))) 2 + 56x + 400x2 + 736x3 = 2((1 + 10x + (1 * 14x + 10x * 14x) + 48x2 * (1 + 10x))) 2 + 56x + 400x2 + 736x3 = 2((1 + 10x + (14x + 140x2) + 48x2 * (1 + 10x))) 2 + 56x + 400x2 + 736x3 = 2((1 + 10x + 14x + 140x2 + (1 * 48x2 + 10x * 48x2))) 2 + 56x + 400x2 + 736x3 = 2((1 + 10x + 14x + 140x2 + (48x2 + 480x3))) Combine like terms: 10x + 14x = 24x 2 + 56x + 400x2 + 736x3 = 2((1 + 24x + 140x2 + 48x2 + 480x3)) Combine like terms: 140x2 + 48x2 = 188x2 2 + 56x + 400x2 + 736x3 = 2((1 + 24x + 188x2 + 480x3)) 2 + 56x + 400x2 + 736x3 = (1 * 2 + 24x * 2 + 188x2 * 2 + 480x3 * 2) 2 + 56x + 400x2 + 736x3 = (2 + 48x + 376x2 + 960x3) Add '-2' to each side of the equation. 2 + 56x + 400x2 + -2 + 736x3 = 2 + 48x + 376x2 + -2 + 960x3 Reorder the terms: 2 + -2 + 56x + 400x2 + 736x3 = 2 + 48x + 376x2 + -2 + 960x3 Combine like terms: 2 + -2 = 0 0 + 56x + 400x2 + 736x3 = 2 + 48x + 376x2 + -2 + 960x3 56x + 400x2 + 736x3 = 2 + 48x + 376x2 + -2 + 960x3 Reorder the terms: 56x + 400x2 + 736x3 = 2 + -2 + 48x + 376x2 + 960x3 Combine like terms: 2 + -2 = 0 56x + 400x2 + 736x3 = 0 + 48x + 376x2 + 960x3 56x + 400x2 + 736x3 = 48x + 376x2 + 960x3 Solving 56x + 400x2 + 736x3 = 48x + 376x2 + 960x3 Solving for variable 'x'. Reorder the terms: 56x + -48x + 400x2 + -376x2 + 736x3 + -960x3 = 48x + 376x2 + 960x3 + -48x + -376x2 + -960x3 Combine like terms: 56x + -48x = 8x 8x + 400x2 + -376x2 + 736x3 + -960x3 = 48x + 376x2 + 960x3 + -48x + -376x2 + -960x3 Combine like terms: 400x2 + -376x2 = 24x2 8x + 24x2 + 736x3 + -960x3 = 48x + 376x2 + 960x3 + -48x + -376x2 + -960x3 Combine like terms: 736x3 + -960x3 = -224x3 8x + 24x2 + -224x3 = 48x + 376x2 + 960x3 + -48x + -376x2 + -960x3 Reorder the terms: 8x + 24x2 + -224x3 = 48x + -48x + 376x2 + -376x2 + 960x3 + -960x3 Combine like terms: 48x + -48x = 0 8x + 24x2 + -224x3 = 0 + 376x2 + -376x2 + 960x3 + -960x3 8x + 24x2 + -224x3 = 376x2 + -376x2 + 960x3 + -960x3 Combine like terms: 376x2 + -376x2 = 0 8x + 24x2 + -224x3 = 0 + 960x3 + -960x3 8x + 24x2 + -224x3 = 960x3 + -960x3 Combine like terms: 960x3 + -960x3 = 0 8x + 24x2 + -224x3 = 0 Factor out the Greatest Common Factor (GCF), '8x'. 8x(1 + 3x + -28x2) = 0 Factor a trinomial. 8x((1 + -4x)(1 + 7x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 3
Set the factor '(1 + 7x)' equal to zero and attempt to solve: Simplifying 1 + 7x = 0 Solving 1 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7x = 0 + -1 7x = 0 + -1 Combine like terms: 0 + -1 = -1 7x = -1 Divide each side by '7'. x = -0.1428571429 Simplifying x = -0.1428571429Solution
x = {0, 0.25, -0.1428571429}
| 8x-(3x-5)=30 | | 5(p+7)=2p+7 | | 18n=50+10(n) | | (16-4*3)-12= | | x^2+4116=91x | | 1000x^2-181x+8.1=0 | | 10000x^2-1801x+81=0 | | 10000x^2-1800x+81=0 | | 100x^2-181x+8.1=0 | | 4sin(x)=3cos(x) | | Log(2x+1)-log(x+1)=1 | | 36x^2-65x+25=0 | | 96+(-85)= | | 6xn=42 | | 25+2-9+1= | | 12*17-8*7= | | -6(p-3)=9 | | 61-6*4= | | 29*21+29= | | 3(m-7)=4(m-3) | | 8(x-5)=-16 | | x*(x-6)=1360 | | 2m+5=3m-4 | | 6(3m-7)=-18 | | An=n(2-n) | | 4p+2.3=9 | | 2x-20=-34+4x | | 4n-40=7(-2h+2) | | x-0.8=9.76 | | (2lnx-2)/x^2=0 | | 9(7y-2)= | | an=12+-3n |