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Simplifying 2(x + 7)(x + -3) + -1x(x + 7) = 140 Reorder the terms: 2(7 + x)(x + -3) + -1x(x + 7) = 140 Reorder the terms: 2(7 + x)(-3 + x) + -1x(x + 7) = 140 Multiply (7 + x) * (-3 + x) 2(7(-3 + x) + x(-3 + x)) + -1x(x + 7) = 140 2((-3 * 7 + x * 7) + x(-3 + x)) + -1x(x + 7) = 140 2((-21 + 7x) + x(-3 + x)) + -1x(x + 7) = 140 2(-21 + 7x + (-3 * x + x * x)) + -1x(x + 7) = 140 2(-21 + 7x + (-3x + x2)) + -1x(x + 7) = 140 Combine like terms: 7x + -3x = 4x 2(-21 + 4x + x2) + -1x(x + 7) = 140 (-21 * 2 + 4x * 2 + x2 * 2) + -1x(x + 7) = 140 (-42 + 8x + 2x2) + -1x(x + 7) = 140 Reorder the terms: -42 + 8x + 2x2 + -1x(7 + x) = 140 -42 + 8x + 2x2 + (7 * -1x + x * -1x) = 140 -42 + 8x + 2x2 + (-7x + -1x2) = 140 Reorder the terms: -42 + 8x + -7x + 2x2 + -1x2 = 140 Combine like terms: 8x + -7x = 1x -42 + 1x + 2x2 + -1x2 = 140 Combine like terms: 2x2 + -1x2 = 1x2 -42 + 1x + 1x2 = 140 Solving -42 + 1x + 1x2 = 140 Solving for variable 'x'. Reorder the terms: -42 + -140 + 1x + 1x2 = 140 + -140 Combine like terms: -42 + -140 = -182 -182 + 1x + 1x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -182 + 1x + 1x2 = 0 Factor a trinomial. (-14 + -1x)(13 + -1x) = 0Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14Subproblem 2
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 = 13Solution
x = {-14, 13}
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