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Simplifying (x + 2)(x + -6) = 6x + 12 Reorder the terms: (2 + x)(x + -6) = 6x + 12 Reorder the terms: (2 + x)(-6 + x) = 6x + 12 Multiply (2 + x) * (-6 + x) (2(-6 + x) + x(-6 + x)) = 6x + 12 ((-6 * 2 + x * 2) + x(-6 + x)) = 6x + 12 ((-12 + 2x) + x(-6 + x)) = 6x + 12 (-12 + 2x + (-6 * x + x * x)) = 6x + 12 (-12 + 2x + (-6x + x2)) = 6x + 12 Combine like terms: 2x + -6x = -4x (-12 + -4x + x2) = 6x + 12 Reorder the terms: -12 + -4x + x2 = 12 + 6x Solving -12 + -4x + x2 = 12 + 6x Solving for variable 'x'. Reorder the terms: -12 + -12 + -4x + -6x + x2 = 12 + 6x + -12 + -6x Combine like terms: -12 + -12 = -24 -24 + -4x + -6x + x2 = 12 + 6x + -12 + -6x Combine like terms: -4x + -6x = -10x -24 + -10x + x2 = 12 + 6x + -12 + -6x Reorder the terms: -24 + -10x + x2 = 12 + -12 + 6x + -6x Combine like terms: 12 + -12 = 0 -24 + -10x + x2 = 0 + 6x + -6x -24 + -10x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -24 + -10x + x2 = 0 Factor a trinomial. (-2 + -1x)(12 + -1x) = 0Subproblem 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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {-2, 12}
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