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Simplifying (x + 5)(x + 2)(x2 + -4) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Reorder the terms: (5 + x)(x + 2)(x2 + -4) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Reorder the terms: (5 + x)(2 + x)(x2 + -4) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Reorder the terms: (5 + x)(2 + x)(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Multiply (5 + x) * (2 + x) (5(2 + x) + x(2 + x))(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) ((2 * 5 + x * 5) + x(2 + x))(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) ((10 + 5x) + x(2 + x))(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) (10 + 5x + (2 * x + x * x))(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) (10 + 5x + (2x + x2))(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Combine like terms: 5x + 2x = 7x (10 + 7x + x2)(-4 + x2) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Multiply (10 + 7x + x2) * (-4 + x2) (10(-4 + x2) + 7x * (-4 + x2) + x2(-4 + x2)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) ((-4 * 10 + x2 * 10) + 7x * (-4 + x2) + x2(-4 + x2)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) ((-40 + 10x2) + 7x * (-4 + x2) + x2(-4 + x2)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) (-40 + 10x2 + (-4 * 7x + x2 * 7x) + x2(-4 + x2)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) (-40 + 10x2 + (-28x + 7x3) + x2(-4 + x2)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) (-40 + 10x2 + -28x + 7x3 + (-4 * x2 + x2 * x2)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) (-40 + 10x2 + -28x + 7x3 + (-4x2 + x4)) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Reorder the terms: (-40 + -28x + 10x2 + -4x2 + 7x3 + x4) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Combine like terms: 10x2 + -4x2 = 6x2 (-40 + -28x + 6x2 + 7x3 + x4) = 5(x + -2)(x2 + -4) + 28(x + -2)(x + 2) Reorder the terms: -40 + -28x + 6x2 + 7x3 + x4 = 5(-2 + x)(x2 + -4) + 28(x + -2)(x + 2) Reorder the terms: -40 + -28x + 6x2 + 7x3 + x4 = 5(-2 + x)(-4 + x2) + 28(x + -2)(x + 2) Multiply (-2 + x) * (-4 + x2) -40 + -28x + 6x2 + 7x3 + x4 = 5(-2(-4 + x2) + x(-4 + x2)) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = 5((-4 * -2 + x2 * -2) + x(-4 + x2)) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = 5((8 + -2x2) + x(-4 + x2)) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = 5(8 + -2x2 + (-4 * x + x2 * x)) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = 5(8 + -2x2 + (-4x + x3)) + 28(x + -2)(x + 2) Reorder the terms: -40 + -28x + 6x2 + 7x3 + x4 = 5(8 + -4x + -2x2 + x3) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = 5(8 + -4x + -2x2 + x3) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = (8 * 5 + -4x * 5 + -2x2 * 5 + x3 * 5) + 28(x + -2)(x + 2) -40 + -28x + 6x2 + 7x3 + x4 = (40 + -20x + -10x2 + 5x3) + 28(x + -2)(x + 2) Reorder the terms: -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-2 + x)(x + 2) Reorder the terms: -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-2 + x)(2 + x) Multiply (-2 + x) * (2 + x) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-2(2 + x) + x(2 + x)) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28((2 * -2 + x * -2) + x(2 + x)) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28((-4 + -2x) + x(2 + x)) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-4 + -2x + (2 * x + x * x)) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-4 + -2x + (2x + x2)) Combine like terms: -2x + 2x = 0 -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-4 + 0 + x2) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + 28(-4 + x2) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + (-4 * 28 + x2 * 28) -40 + -28x + 6x2 + 7x3 + x4 = 40 + -20x + -10x2 + 5x3 + (-112 + 28x2) Reorder the terms: -40 + -28x + 6x2 + 7x3 + x4 = 40 + -112 + -20x + -10x2 + 28x2 + 5x3 Combine like terms: 40 + -112 = -72 -40 + -28x + 6x2 + 7x3 + x4 = -72 + -20x + -10x2 + 28x2 + 5x3 Combine like terms: -10x2 + 28x2 = 18x2 -40 + -28x + 6x2 + 7x3 + x4 = -72 + -20x + 18x2 + 5x3 Solving -40 + -28x + 6x2 + 7x3 + x4 = -72 + -20x + 18x2 + 5x3 Solving for variable 'x'. Reorder the terms: -40 + 72 + -28x + 20x + 6x2 + -18x2 + 7x3 + -5x3 + x4 = -72 + -20x + 18x2 + 5x3 + 72 + 20x + -18x2 + -5x3 Combine like terms: -40 + 72 = 32 32 + -28x + 20x + 6x2 + -18x2 + 7x3 + -5x3 + x4 = -72 + -20x + 18x2 + 5x3 + 72 + 20x + -18x2 + -5x3 Combine like terms: -28x + 20x = -8x 32 + -8x + 6x2 + -18x2 + 7x3 + -5x3 + x4 = -72 + -20x + 18x2 + 5x3 + 72 + 20x + -18x2 + -5x3 Combine like terms: 6x2 + -18x2 = -12x2 32 + -8x + -12x2 + 7x3 + -5x3 + x4 = -72 + -20x + 18x2 + 5x3 + 72 + 20x + -18x2 + -5x3 Combine like terms: 7x3 + -5x3 = 2x3 32 + -8x + -12x2 + 2x3 + x4 = -72 + -20x + 18x2 + 5x3 + 72 + 20x + -18x2 + -5x3 Reorder the terms: 32 + -8x + -12x2 + 2x3 + x4 = -72 + 72 + -20x + 20x + 18x2 + -18x2 + 5x3 + -5x3 Combine like terms: -72 + 72 = 0 32 + -8x + -12x2 + 2x3 + x4 = 0 + -20x + 20x + 18x2 + -18x2 + 5x3 + -5x3 32 + -8x + -12x2 + 2x3 + x4 = -20x + 20x + 18x2 + -18x2 + 5x3 + -5x3 Combine like terms: -20x + 20x = 0 32 + -8x + -12x2 + 2x3 + x4 = 0 + 18x2 + -18x2 + 5x3 + -5x3 32 + -8x + -12x2 + 2x3 + x4 = 18x2 + -18x2 + 5x3 + -5x3 Combine like terms: 18x2 + -18x2 = 0 32 + -8x + -12x2 + 2x3 + x4 = 0 + 5x3 + -5x3 32 + -8x + -12x2 + 2x3 + x4 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 32 + -8x + -12x2 + 2x3 + x4 = 0 The solution to this equation could not be determined.
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