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Simplifying (x + -2)(x + 3) + (x + -3)(x + 2) = 4(x + 1) Reorder the terms: (-2 + x)(x + 3) + (x + -3)(x + 2) = 4(x + 1) Reorder the terms: (-2 + x)(3 + x) + (x + -3)(x + 2) = 4(x + 1) Multiply (-2 + x) * (3 + x) (-2(3 + x) + x(3 + x)) + (x + -3)(x + 2) = 4(x + 1) ((3 * -2 + x * -2) + x(3 + x)) + (x + -3)(x + 2) = 4(x + 1) ((-6 + -2x) + x(3 + x)) + (x + -3)(x + 2) = 4(x + 1) (-6 + -2x + (3 * x + x * x)) + (x + -3)(x + 2) = 4(x + 1) (-6 + -2x + (3x + x2)) + (x + -3)(x + 2) = 4(x + 1) Combine like terms: -2x + 3x = 1x (-6 + 1x + x2) + (x + -3)(x + 2) = 4(x + 1) Reorder the terms: -6 + 1x + x2 + (-3 + x)(x + 2) = 4(x + 1) Reorder the terms: -6 + 1x + x2 + (-3 + x)(2 + x) = 4(x + 1) Multiply (-3 + x) * (2 + x) -6 + 1x + x2 + (-3(2 + x) + x(2 + x)) = 4(x + 1) -6 + 1x + x2 + ((2 * -3 + x * -3) + x(2 + x)) = 4(x + 1) -6 + 1x + x2 + ((-6 + -3x) + x(2 + x)) = 4(x + 1) -6 + 1x + x2 + (-6 + -3x + (2 * x + x * x)) = 4(x + 1) -6 + 1x + x2 + (-6 + -3x + (2x + x2)) = 4(x + 1) Combine like terms: -3x + 2x = -1x -6 + 1x + x2 + (-6 + -1x + x2) = 4(x + 1) Reorder the terms: -6 + -6 + 1x + -1x + x2 + x2 = 4(x + 1) Combine like terms: -6 + -6 = -12 -12 + 1x + -1x + x2 + x2 = 4(x + 1) Combine like terms: 1x + -1x = 0 -12 + 0 + x2 + x2 = 4(x + 1) -12 + x2 + x2 = 4(x + 1) Combine like terms: x2 + x2 = 2x2 -12 + 2x2 = 4(x + 1) Reorder the terms: -12 + 2x2 = 4(1 + x) -12 + 2x2 = (1 * 4 + x * 4) -12 + 2x2 = (4 + 4x) Solving -12 + 2x2 = 4 + 4x Solving for variable 'x'. Reorder the terms: -12 + -4 + -4x + 2x2 = 4 + 4x + -4 + -4x Combine like terms: -12 + -4 = -16 -16 + -4x + 2x2 = 4 + 4x + -4 + -4x Reorder the terms: -16 + -4x + 2x2 = 4 + -4 + 4x + -4x Combine like terms: 4 + -4 = 0 -16 + -4x + 2x2 = 0 + 4x + -4x -16 + -4x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -16 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -2x + x2) = 0 Factor a trinomial. 2((-2 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2, 4}
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