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Simplifying 2(x + 3)(x + -1) = (x + 3) * x + 234 Reorder the terms: 2(3 + x)(x + -1) = (x + 3) * x + 234 Reorder the terms: 2(3 + x)(-1 + x) = (x + 3) * x + 234 Multiply (3 + x) * (-1 + x) 2(3(-1 + x) + x(-1 + x)) = (x + 3) * x + 234 2((-1 * 3 + x * 3) + x(-1 + x)) = (x + 3) * x + 234 2((-3 + 3x) + x(-1 + x)) = (x + 3) * x + 234 2(-3 + 3x + (-1 * x + x * x)) = (x + 3) * x + 234 2(-3 + 3x + (-1x + x2)) = (x + 3) * x + 234 Combine like terms: 3x + -1x = 2x 2(-3 + 2x + x2) = (x + 3) * x + 234 (-3 * 2 + 2x * 2 + x2 * 2) = (x + 3) * x + 234 (-6 + 4x + 2x2) = (x + 3) * x + 234 Reorder the terms: -6 + 4x + 2x2 = (3 + x) * x + 234 Reorder the terms for easier multiplication: -6 + 4x + 2x2 = x(3 + x) + 234 -6 + 4x + 2x2 = (3 * x + x * x) + 234 -6 + 4x + 2x2 = (3x + x2) + 234 Reorder the terms: -6 + 4x + 2x2 = 234 + 3x + x2 Solving -6 + 4x + 2x2 = 234 + 3x + x2 Solving for variable 'x'. Reorder the terms: -6 + -234 + 4x + -3x + 2x2 + -1x2 = 234 + 3x + x2 + -234 + -3x + -1x2 Combine like terms: -6 + -234 = -240 -240 + 4x + -3x + 2x2 + -1x2 = 234 + 3x + x2 + -234 + -3x + -1x2 Combine like terms: 4x + -3x = 1x -240 + 1x + 2x2 + -1x2 = 234 + 3x + x2 + -234 + -3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -240 + 1x + 1x2 = 234 + 3x + x2 + -234 + -3x + -1x2 Reorder the terms: -240 + 1x + 1x2 = 234 + -234 + 3x + -3x + x2 + -1x2 Combine like terms: 234 + -234 = 0 -240 + 1x + 1x2 = 0 + 3x + -3x + x2 + -1x2 -240 + 1x + 1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -240 + 1x + 1x2 = 0 + x2 + -1x2 -240 + 1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -240 + 1x + 1x2 = 0 Factor a trinomial. (-16 + -1x)(15 + -1x) = 0Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve: Simplifying -16 + -1x = 0 Solving -16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x = 0 + 16 -1x = 0 + 16 Combine like terms: 0 + 16 = 16 -1x = 16 Divide each side by '-1'. x = -16 Simplifying x = -16Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-16, 15}
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