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Simplifying (x + 6)(x + -2) = (2x + 4)(x + -2) Reorder the terms: (6 + x)(x + -2) = (2x + 4)(x + -2) Reorder the terms: (6 + x)(-2 + x) = (2x + 4)(x + -2) Multiply (6 + x) * (-2 + x) (6(-2 + x) + x(-2 + x)) = (2x + 4)(x + -2) ((-2 * 6 + x * 6) + x(-2 + x)) = (2x + 4)(x + -2) ((-12 + 6x) + x(-2 + x)) = (2x + 4)(x + -2) (-12 + 6x + (-2 * x + x * x)) = (2x + 4)(x + -2) (-12 + 6x + (-2x + x2)) = (2x + 4)(x + -2) Combine like terms: 6x + -2x = 4x (-12 + 4x + x2) = (2x + 4)(x + -2) Reorder the terms: -12 + 4x + x2 = (4 + 2x)(x + -2) Reorder the terms: -12 + 4x + x2 = (4 + 2x)(-2 + x) Multiply (4 + 2x) * (-2 + x) -12 + 4x + x2 = (4(-2 + x) + 2x * (-2 + x)) -12 + 4x + x2 = ((-2 * 4 + x * 4) + 2x * (-2 + x)) -12 + 4x + x2 = ((-8 + 4x) + 2x * (-2 + x)) -12 + 4x + x2 = (-8 + 4x + (-2 * 2x + x * 2x)) -12 + 4x + x2 = (-8 + 4x + (-4x + 2x2)) Combine like terms: 4x + -4x = 0 -12 + 4x + x2 = (-8 + 0 + 2x2) -12 + 4x + x2 = (-8 + 2x2) Solving -12 + 4x + x2 = -8 + 2x2 Solving for variable 'x'. Reorder the terms: -12 + 8 + 4x + x2 + -2x2 = -8 + 2x2 + 8 + -2x2 Combine like terms: -12 + 8 = -4 -4 + 4x + x2 + -2x2 = -8 + 2x2 + 8 + -2x2 Combine like terms: x2 + -2x2 = -1x2 -4 + 4x + -1x2 = -8 + 2x2 + 8 + -2x2 Reorder the terms: -4 + 4x + -1x2 = -8 + 8 + 2x2 + -2x2 Combine like terms: -8 + 8 = 0 -4 + 4x + -1x2 = 0 + 2x2 + -2x2 -4 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + 4x + -1x2 = 0 Factor a trinomial. (-2 + x)(2 + -1x) = 0Subproblem 1
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 2
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 = 2Solution
x = {2, 2}
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