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Simplifying 2(x + 9)(x + -4) = x(x + 9) + 168 Reorder the terms: 2(9 + x)(x + -4) = x(x + 9) + 168 Reorder the terms: 2(9 + x)(-4 + x) = x(x + 9) + 168 Multiply (9 + x) * (-4 + x) 2(9(-4 + x) + x(-4 + x)) = x(x + 9) + 168 2((-4 * 9 + x * 9) + x(-4 + x)) = x(x + 9) + 168 2((-36 + 9x) + x(-4 + x)) = x(x + 9) + 168 2(-36 + 9x + (-4 * x + x * x)) = x(x + 9) + 168 2(-36 + 9x + (-4x + x2)) = x(x + 9) + 168 Combine like terms: 9x + -4x = 5x 2(-36 + 5x + x2) = x(x + 9) + 168 (-36 * 2 + 5x * 2 + x2 * 2) = x(x + 9) + 168 (-72 + 10x + 2x2) = x(x + 9) + 168 Reorder the terms: -72 + 10x + 2x2 = x(9 + x) + 168 -72 + 10x + 2x2 = (9 * x + x * x) + 168 -72 + 10x + 2x2 = (9x + x2) + 168 Reorder the terms: -72 + 10x + 2x2 = 168 + 9x + x2 Solving -72 + 10x + 2x2 = 168 + 9x + x2 Solving for variable 'x'. Reorder the terms: -72 + -168 + 10x + -9x + 2x2 + -1x2 = 168 + 9x + x2 + -168 + -9x + -1x2 Combine like terms: -72 + -168 = -240 -240 + 10x + -9x + 2x2 + -1x2 = 168 + 9x + x2 + -168 + -9x + -1x2 Combine like terms: 10x + -9x = 1x -240 + 1x + 2x2 + -1x2 = 168 + 9x + x2 + -168 + -9x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -240 + 1x + 1x2 = 168 + 9x + x2 + -168 + -9x + -1x2 Reorder the terms: -240 + 1x + 1x2 = 168 + -168 + 9x + -9x + x2 + -1x2 Combine like terms: 168 + -168 = 0 -240 + 1x + 1x2 = 0 + 9x + -9x + x2 + -1x2 -240 + 1x + 1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 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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