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Simplifying (x + 2)(x + -3) = 176 Reorder the terms: (2 + x)(x + -3) = 176 Reorder the terms: (2 + x)(-3 + x) = 176 Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = 176 ((-3 * 2 + x * 2) + x(-3 + x)) = 176 ((-6 + 2x) + x(-3 + x)) = 176 (-6 + 2x + (-3 * x + x * x)) = 176 (-6 + 2x + (-3x + x2)) = 176 Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = 176 Solving -6 + -1x + x2 = 176 Solving for variable 'x'. Reorder the terms: -6 + -176 + -1x + x2 = 176 + -176 Combine like terms: -6 + -176 = -182 -182 + -1x + x2 = 176 + -176 Combine like terms: 176 + -176 = 0 -182 + -1x + x2 = 0 Factor a trinomial. (-13 + -1x)(14 + -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 '(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 = 14Solution
x = {-13, 14}
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