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Simplifying (x + 1)(x + -1)(x + -2) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Reorder the terms: (1 + x)(x + -1)(x + -2) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Reorder the terms: (1 + x)(-1 + x)(x + -2) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Reorder the terms: (1 + x)(-1 + x)(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Multiply (1 + x) * (-1 + x) (1(-1 + x) + x(-1 + x))(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 ((-1 * 1 + x * 1) + x(-1 + x))(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 ((-1 + 1x) + x(-1 + x))(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 (-1 + 1x + (-1 * x + x * x))(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 (-1 + 1x + (-1x + x2))(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Combine like terms: 1x + -1x = 0 (-1 + 0 + x2)(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 (-1 + x2)(-2 + x) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Multiply (-1 + x2) * (-2 + x) (-1(-2 + x) + x2(-2 + x)) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 ((-2 * -1 + x * -1) + x2(-2 + x)) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 ((2 + -1x) + x2(-2 + x)) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 (2 + -1x + (-2 * x2 + x * x2)) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 (2 + -1x + (-2x2 + x3)) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 (2 + -1x + -2x2 + x3) + -1(x2 + 7x)(x + -4) + -2 + -2x = 0 Reorder the terms: 2 + -1x + -2x2 + x3 + -1(7x + x2)(x + -4) + -2 + -2x = 0 Reorder the terms: 2 + -1x + -2x2 + x3 + -1(7x + x2)(-4 + x) + -2 + -2x = 0 Multiply (7x + x2) * (-4 + x) 2 + -1x + -2x2 + x3 + -1(7x * (-4 + x) + x2(-4 + x)) + -2 + -2x = 0 2 + -1x + -2x2 + x3 + -1((-4 * 7x + x * 7x) + x2(-4 + x)) + -2 + -2x = 0 2 + -1x + -2x2 + x3 + -1((-28x + 7x2) + x2(-4 + x)) + -2 + -2x = 0 2 + -1x + -2x2 + x3 + -1(-28x + 7x2 + (-4 * x2 + x * x2)) + -2 + -2x = 0 2 + -1x + -2x2 + x3 + -1(-28x + 7x2 + (-4x2 + x3)) + -2 + -2x = 0 Combine like terms: 7x2 + -4x2 = 3x2 2 + -1x + -2x2 + x3 + -1(-28x + 3x2 + x3) + -2 + -2x = 0 2 + -1x + -2x2 + x3 + (-28x * -1 + 3x2 * -1 + x3 * -1) + -2 + -2x = 0 2 + -1x + -2x2 + x3 + (28x + -3x2 + -1x3) + -2 + -2x = 0 Reorder the terms: 2 + -2 + -1x + 28x + -2x + -2x2 + -3x2 + x3 + -1x3 = 0 Combine like terms: 2 + -2 = 0 0 + -1x + 28x + -2x + -2x2 + -3x2 + x3 + -1x3 = 0 -1x + 28x + -2x + -2x2 + -3x2 + x3 + -1x3 = 0 Combine like terms: -1x + 28x = 27x 27x + -2x + -2x2 + -3x2 + x3 + -1x3 = 0 Combine like terms: 27x + -2x = 25x 25x + -2x2 + -3x2 + x3 + -1x3 = 0 Combine like terms: -2x2 + -3x2 = -5x2 25x + -5x2 + x3 + -1x3 = 0 Combine like terms: x3 + -1x3 = 0 25x + -5x2 + 0 = 0 25x + -5x2 = 0 Solving 25x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(5 + -1x) = 0 Ignore the factor 5.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 '(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 = {0, 5}
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