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Simplifying (7x + 6)((x + 2)(x + -2)) = (6)((x + 2)(x + -2)) Reorder the terms: (6 + 7x)((x + 2)(x + -2)) = (6)((x + 2)(x + -2)) Reorder the terms: (6 + 7x)((2 + x)(x + -2)) = (6)((x + 2)(x + -2)) Reorder the terms: (6 + 7x)((2 + x)(-2 + x)) = (6)((x + 2)(x + -2)) Multiply (2 + x) * (-2 + x) (6 + 7x)((2(-2 + x) + x(-2 + x))) = (6)((x + 2)(x + -2)) (6 + 7x)(((-2 * 2 + x * 2) + x(-2 + x))) = (6)((x + 2)(x + -2)) (6 + 7x)(((-4 + 2x) + x(-2 + x))) = (6)((x + 2)(x + -2)) (6 + 7x)((-4 + 2x + (-2 * x + x * x))) = (6)((x + 2)(x + -2)) (6 + 7x)((-4 + 2x + (-2x + x2))) = (6)((x + 2)(x + -2)) Combine like terms: 2x + -2x = 0 (6 + 7x)((-4 + 0 + x2)) = (6)((x + 2)(x + -2)) (6 + 7x)((-4 + x2)) = (6)((x + 2)(x + -2)) Multiply (6 + 7x) * (-4 + x2) (6(-4 + x2) + 7x * (-4 + x2)) = (6)((x + 2)(x + -2)) ((-4 * 6 + x2 * 6) + 7x * (-4 + x2)) = (6)((x + 2)(x + -2)) ((-24 + 6x2) + 7x * (-4 + x2)) = (6)((x + 2)(x + -2)) (-24 + 6x2 + (-4 * 7x + x2 * 7x)) = (6)((x + 2)(x + -2)) (-24 + 6x2 + (-28x + 7x3)) = (6)((x + 2)(x + -2)) Reorder the terms: (-24 + -28x + 6x2 + 7x3) = (6)((x + 2)(x + -2)) (-24 + -28x + 6x2 + 7x3) = (6)((x + 2)(x + -2)) Reorder the terms: -24 + -28x + 6x2 + 7x3 = 6((2 + x)(x + -2)) Reorder the terms: -24 + -28x + 6x2 + 7x3 = 6((2 + x)(-2 + x)) Multiply (2 + x) * (-2 + x) -24 + -28x + 6x2 + 7x3 = 6((2(-2 + x) + x(-2 + x))) -24 + -28x + 6x2 + 7x3 = 6(((-2 * 2 + x * 2) + x(-2 + x))) -24 + -28x + 6x2 + 7x3 = 6(((-4 + 2x) + x(-2 + x))) -24 + -28x + 6x2 + 7x3 = 6((-4 + 2x + (-2 * x + x * x))) -24 + -28x + 6x2 + 7x3 = 6((-4 + 2x + (-2x + x2))) Combine like terms: 2x + -2x = 0 -24 + -28x + 6x2 + 7x3 = 6((-4 + 0 + x2)) -24 + -28x + 6x2 + 7x3 = 6((-4 + x2)) -24 + -28x + 6x2 + 7x3 = (-4 * 6 + x2 * 6) -24 + -28x + 6x2 + 7x3 = (-24 + 6x2) Add '24' to each side of the equation. -24 + -28x + 6x2 + 24 + 7x3 = -24 + 24 + 6x2 Reorder the terms: -24 + 24 + -28x + 6x2 + 7x3 = -24 + 24 + 6x2 Combine like terms: -24 + 24 = 0 0 + -28x + 6x2 + 7x3 = -24 + 24 + 6x2 -28x + 6x2 + 7x3 = -24 + 24 + 6x2 Combine like terms: -24 + 24 = 0 -28x + 6x2 + 7x3 = 0 + 6x2 -28x + 6x2 + 7x3 = 6x2 Add '-6x2' to each side of the equation. -28x + 6x2 + -6x2 + 7x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -28x + 0 + 7x3 = 6x2 + -6x2 -28x + 7x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -28x + 7x3 = 0 Solving -28x + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x'. 7x(-4 + x2) = 0 Factor a difference between two squares. 7x((2 + x)(-2 + x)) = 0 Ignore the factor 7.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {0, -2, 2}
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