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Simplifying (3x + -9)(x2 + -4x + -1x + 4) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: (-9 + 3x)(x2 + -4x + -1x + 4) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: (-9 + 3x)(4 + -4x + -1x + x2) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -4x + -1x = -5x (-9 + 3x)(4 + -5x + x2) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Multiply (-9 + 3x) * (4 + -5x + x2) (-9(4 + -5x + x2) + 3x * (4 + -5x + x2)) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) ((4 * -9 + -5x * -9 + x2 * -9) + 3x * (4 + -5x + x2)) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) ((-36 + 45x + -9x2) + 3x * (4 + -5x + x2)) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) (-36 + 45x + -9x2 + (4 * 3x + -5x * 3x + x2 * 3x)) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) (-36 + 45x + -9x2 + (12x + -15x2 + 3x3)) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: (-36 + 45x + 12x + -9x2 + -15x2 + 3x3) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: 45x + 12x = 57x (-36 + 57x + -9x2 + -15x2 + 3x3) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -9x2 + -15x2 = -24x2 (-36 + 57x + -24x2 + 3x3) + (2x + -4)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -36 + 57x + -24x2 + 3x3 + (-4 + 2x)(x2 + -4x + -1x + 4) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -36 + 57x + -24x2 + 3x3 + (-4 + 2x)(4 + -4x + -1x + x2) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -4x + -1x = -5x -36 + 57x + -24x2 + 3x3 + (-4 + 2x)(4 + -5x + x2) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Multiply (-4 + 2x) * (4 + -5x + x2) -36 + 57x + -24x2 + 3x3 + (-4(4 + -5x + x2) + 2x * (4 + -5x + x2)) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) -36 + 57x + -24x2 + 3x3 + ((4 * -4 + -5x * -4 + x2 * -4) + 2x * (4 + -5x + x2)) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) -36 + 57x + -24x2 + 3x3 + ((-16 + 20x + -4x2) + 2x * (4 + -5x + x2)) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) -36 + 57x + -24x2 + 3x3 + (-16 + 20x + -4x2 + (4 * 2x + -5x * 2x + x2 * 2x)) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) -36 + 57x + -24x2 + 3x3 + (-16 + 20x + -4x2 + (8x + -10x2 + 2x3)) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -36 + 57x + -24x2 + 3x3 + (-16 + 20x + 8x + -4x2 + -10x2 + 2x3) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: 20x + 8x = 28x -36 + 57x + -24x2 + 3x3 + (-16 + 28x + -4x2 + -10x2 + 2x3) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -4x2 + -10x2 = -14x2 -36 + 57x + -24x2 + 3x3 + (-16 + 28x + -14x2 + 2x3) = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -36 + -16 + 57x + 28x + -24x2 + -14x2 + 3x3 + 2x3 = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -36 + -16 = -52 -52 + 57x + 28x + -24x2 + -14x2 + 3x3 + 2x3 = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: 57x + 28x = 85x -52 + 85x + -24x2 + -14x2 + 3x3 + 2x3 = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -24x2 + -14x2 = -38x2 -52 + 85x + -38x2 + 3x3 + 2x3 = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: 3x3 + 2x3 = 5x3 -52 + 85x + -38x2 + 5x3 = (4x + -12)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -52 + 85x + -38x2 + 5x3 = (-12 + 4x)(x2 + -4x + -2x + 8) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -52 + 85x + -38x2 + 5x3 = (-12 + 4x)(8 + -4x + -2x + x2) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -4x + -2x = -6x -52 + 85x + -38x2 + 5x3 = (-12 + 4x)(8 + -6x + x2) + (x + -3)(x2 + -1x + -2x + 2) Multiply (-12 + 4x) * (8 + -6x + x2) -52 + 85x + -38x2 + 5x3 = (-12(8 + -6x + x2) + 4x * (8 + -6x + x2)) + (x + -3)(x2 + -1x + -2x + 2) -52 + 85x + -38x2 + 5x3 = ((8 * -12 + -6x * -12 + x2 * -12) + 4x * (8 + -6x + x2)) + (x + -3)(x2 + -1x + -2x + 2) -52 + 85x + -38x2 + 5x3 = ((-96 + 72x + -12x2) + 4x * (8 + -6x + x2)) + (x + -3)(x2 + -1x + -2x + 2) -52 + 85x + -38x2 + 5x3 = (-96 + 72x + -12x2 + (8 * 4x + -6x * 4x + x2 * 4x)) + (x + -3)(x2 + -1x + -2x + 2) -52 + 85x + -38x2 + 5x3 = (-96 + 72x + -12x2 + (32x + -24x2 + 4x3)) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -52 + 85x + -38x2 + 5x3 = (-96 + 72x + 32x + -12x2 + -24x2 + 4x3) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: 72x + 32x = 104x -52 + 85x + -38x2 + 5x3 = (-96 + 104x + -12x2 + -24x2 + 4x3) + (x + -3)(x2 + -1x + -2x + 2) Combine like terms: -12x2 + -24x2 = -36x2 -52 + 85x + -38x2 + 5x3 = (-96 + 104x + -36x2 + 4x3) + (x + -3)(x2 + -1x + -2x + 2) Reorder the terms: -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-3 + x)(x2 + -1x + -2x + 2) Reorder the terms: -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-3 + x)(2 + -1x + -2x + x2) Combine like terms: -1x + -2x = -3x -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-3 + x)(2 + -3x + x2) Multiply (-3 + x) * (2 + -3x + x2) -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-3(2 + -3x + x2) + x(2 + -3x + x2)) -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + ((2 * -3 + -3x * -3 + x2 * -3) + x(2 + -3x + x2)) -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + ((-6 + 9x + -3x2) + x(2 + -3x + x2)) -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-6 + 9x + -3x2 + (2 * x + -3x * x + x2 * x)) -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-6 + 9x + -3x2 + (2x + -3x2 + x3)) Reorder the terms: -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-6 + 9x + 2x + -3x2 + -3x2 + x3) Combine like terms: 9x + 2x = 11x -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-6 + 11x + -3x2 + -3x2 + x3) Combine like terms: -3x2 + -3x2 = -6x2 -52 + 85x + -38x2 + 5x3 = -96 + 104x + -36x2 + 4x3 + (-6 + 11x + -6x2 + x3) Reorder the terms: -52 + 85x + -38x2 + 5x3 = -96 + -6 + 104x + 11x + -36x2 + -6x2 + 4x3 + x3 Combine like terms: -96 + -6 = -102 -52 + 85x + -38x2 + 5x3 = -102 + 104x + 11x + -36x2 + -6x2 + 4x3 + x3 Combine like terms: 104x + 11x = 115x -52 + 85x + -38x2 + 5x3 = -102 + 115x + -36x2 + -6x2 + 4x3 + x3 Combine like terms: -36x2 + -6x2 = -42x2 -52 + 85x + -38x2 + 5x3 = -102 + 115x + -42x2 + 4x3 + x3 Combine like terms: 4x3 + x3 = 5x3 -52 + 85x + -38x2 + 5x3 = -102 + 115x + -42x2 + 5x3 Add '-5x3' to each side of the equation. -52 + 85x + -38x2 + 5x3 + -5x3 = -102 + 115x + -42x2 + 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -52 + 85x + -38x2 + 0 = -102 + 115x + -42x2 + 5x3 + -5x3 -52 + 85x + -38x2 = -102 + 115x + -42x2 + 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -52 + 85x + -38x2 = -102 + 115x + -42x2 + 0 -52 + 85x + -38x2 = -102 + 115x + -42x2 Solving -52 + 85x + -38x2 = -102 + 115x + -42x2 Solving for variable 'x'. Reorder the terms: -52 + 102 + 85x + -115x + -38x2 + 42x2 = -102 + 115x + -42x2 + 102 + -115x + 42x2 Combine like terms: -52 + 102 = 50 50 + 85x + -115x + -38x2 + 42x2 = -102 + 115x + -42x2 + 102 + -115x + 42x2 Combine like terms: 85x + -115x = -30x 50 + -30x + -38x2 + 42x2 = -102 + 115x + -42x2 + 102 + -115x + 42x2 Combine like terms: -38x2 + 42x2 = 4x2 50 + -30x + 4x2 = -102 + 115x + -42x2 + 102 + -115x + 42x2 Reorder the terms: 50 + -30x + 4x2 = -102 + 102 + 115x + -115x + -42x2 + 42x2 Combine like terms: -102 + 102 = 0 50 + -30x + 4x2 = 0 + 115x + -115x + -42x2 + 42x2 50 + -30x + 4x2 = 115x + -115x + -42x2 + 42x2 Combine like terms: 115x + -115x = 0 50 + -30x + 4x2 = 0 + -42x2 + 42x2 50 + -30x + 4x2 = -42x2 + 42x2 Combine like terms: -42x2 + 42x2 = 0 50 + -30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -15x + 2x2) = 0 Factor a trinomial. 2((5 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {2.5, 5}
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