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Simplifying (x + -3)(x + 2) = 126 Reorder the terms: (-3 + x)(x + 2) = 126 Reorder the terms: (-3 + x)(2 + x) = 126 Multiply (-3 + x) * (2 + x) (-3(2 + x) + x(2 + x)) = 126 ((2 * -3 + x * -3) + x(2 + x)) = 126 ((-6 + -3x) + x(2 + x)) = 126 (-6 + -3x + (2 * x + x * x)) = 126 (-6 + -3x + (2x + x2)) = 126 Combine like terms: -3x + 2x = -1x (-6 + -1x + x2) = 126 Solving -6 + -1x + x2 = 126 Solving for variable 'x'. Reorder the terms: -6 + -126 + -1x + x2 = 126 + -126 Combine like terms: -6 + -126 = -132 -132 + -1x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -132 + -1x + x2 = 0 Factor a trinomial. (-11 + -1x)(12 + -1x) = 0Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 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 = {-11, 12}
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