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Simplifying 2(x + 7)(x + -3) + -1x(x + 7) = 90 Reorder the terms: 2(7 + x)(x + -3) + -1x(x + 7) = 90 Reorder the terms: 2(7 + x)(-3 + x) + -1x(x + 7) = 90 Multiply (7 + x) * (-3 + x) 2(7(-3 + x) + x(-3 + x)) + -1x(x + 7) = 90 2((-3 * 7 + x * 7) + x(-3 + x)) + -1x(x + 7) = 90 2((-21 + 7x) + x(-3 + x)) + -1x(x + 7) = 90 2(-21 + 7x + (-3 * x + x * x)) + -1x(x + 7) = 90 2(-21 + 7x + (-3x + x2)) + -1x(x + 7) = 90 Combine like terms: 7x + -3x = 4x 2(-21 + 4x + x2) + -1x(x + 7) = 90 (-21 * 2 + 4x * 2 + x2 * 2) + -1x(x + 7) = 90 (-42 + 8x + 2x2) + -1x(x + 7) = 90 Reorder the terms: -42 + 8x + 2x2 + -1x(7 + x) = 90 -42 + 8x + 2x2 + (7 * -1x + x * -1x) = 90 -42 + 8x + 2x2 + (-7x + -1x2) = 90 Reorder the terms: -42 + 8x + -7x + 2x2 + -1x2 = 90 Combine like terms: 8x + -7x = 1x -42 + 1x + 2x2 + -1x2 = 90 Combine like terms: 2x2 + -1x2 = 1x2 -42 + 1x + 1x2 = 90 Solving -42 + 1x + 1x2 = 90 Solving for variable 'x'. Reorder the terms: -42 + -90 + 1x + 1x2 = 90 + -90 Combine like terms: -42 + -90 = -132 -132 + 1x + 1x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -132 + 1x + 1x2 = 0 Factor a trinomial. (-12 + -1x)(11 + -1x) = 0Subproblem 1
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 = -12Subproblem 2
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 = 11Solution
x = {-12, 11}
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