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Simplifying 2(x + 3)(x + -1) + -1x(x + 3) = 176 Reorder the terms: 2(3 + x)(x + -1) + -1x(x + 3) = 176 Reorder the terms: 2(3 + x)(-1 + x) + -1x(x + 3) = 176 Multiply (3 + x) * (-1 + x) 2(3(-1 + x) + x(-1 + x)) + -1x(x + 3) = 176 2((-1 * 3 + x * 3) + x(-1 + x)) + -1x(x + 3) = 176 2((-3 + 3x) + x(-1 + x)) + -1x(x + 3) = 176 2(-3 + 3x + (-1 * x + x * x)) + -1x(x + 3) = 176 2(-3 + 3x + (-1x + x2)) + -1x(x + 3) = 176 Combine like terms: 3x + -1x = 2x 2(-3 + 2x + x2) + -1x(x + 3) = 176 (-3 * 2 + 2x * 2 + x2 * 2) + -1x(x + 3) = 176 (-6 + 4x + 2x2) + -1x(x + 3) = 176 Reorder the terms: -6 + 4x + 2x2 + -1x(3 + x) = 176 -6 + 4x + 2x2 + (3 * -1x + x * -1x) = 176 -6 + 4x + 2x2 + (-3x + -1x2) = 176 Reorder the terms: -6 + 4x + -3x + 2x2 + -1x2 = 176 Combine like terms: 4x + -3x = 1x -6 + 1x + 2x2 + -1x2 = 176 Combine like terms: 2x2 + -1x2 = 1x2 -6 + 1x + 1x2 = 176 Solving -6 + 1x + 1x2 = 176 Solving for variable 'x'. Reorder the terms: -6 + -176 + 1x + 1x2 = 176 + -176 Combine like terms: -6 + -176 = -182 -182 + 1x + 1x2 = 176 + -176 Combine like terms: 176 + -176 = 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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