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Simplifying 2(x + 9)(x + -4) + -1x(x + 9) = 84 Reorder the terms: 2(9 + x)(x + -4) + -1x(x + 9) = 84 Reorder the terms: 2(9 + x)(-4 + x) + -1x(x + 9) = 84 Multiply (9 + x) * (-4 + x) 2(9(-4 + x) + x(-4 + x)) + -1x(x + 9) = 84 2((-4 * 9 + x * 9) + x(-4 + x)) + -1x(x + 9) = 84 2((-36 + 9x) + x(-4 + x)) + -1x(x + 9) = 84 2(-36 + 9x + (-4 * x + x * x)) + -1x(x + 9) = 84 2(-36 + 9x + (-4x + x2)) + -1x(x + 9) = 84 Combine like terms: 9x + -4x = 5x 2(-36 + 5x + x2) + -1x(x + 9) = 84 (-36 * 2 + 5x * 2 + x2 * 2) + -1x(x + 9) = 84 (-72 + 10x + 2x2) + -1x(x + 9) = 84 Reorder the terms: -72 + 10x + 2x2 + -1x(9 + x) = 84 -72 + 10x + 2x2 + (9 * -1x + x * -1x) = 84 -72 + 10x + 2x2 + (-9x + -1x2) = 84 Reorder the terms: -72 + 10x + -9x + 2x2 + -1x2 = 84 Combine like terms: 10x + -9x = 1x -72 + 1x + 2x2 + -1x2 = 84 Combine like terms: 2x2 + -1x2 = 1x2 -72 + 1x + 1x2 = 84 Solving -72 + 1x + 1x2 = 84 Solving for variable 'x'. Reorder the terms: -72 + -84 + 1x + 1x2 = 84 + -84 Combine like terms: -72 + -84 = -156 -156 + 1x + 1x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -156 + 1x + 1x2 = 0 Factor a trinomial. (-13 + -1x)(12 + -1x) = 0Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve: Simplifying -13 + -1x = 0 Solving -13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x = 0 + 13 -1x = 0 + 13 Combine like terms: 0 + 13 = 13 -1x = 13 Divide each side by '-1'. x = -13 Simplifying x = -13Subproblem 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 = {-13, 12}
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