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Simplifying (x + 5)(x + -4) = 36 Reorder the terms: (5 + x)(x + -4) = 36 Reorder the terms: (5 + x)(-4 + x) = 36 Multiply (5 + x) * (-4 + x) (5(-4 + x) + x(-4 + x)) = 36 ((-4 * 5 + x * 5) + x(-4 + x)) = 36 ((-20 + 5x) + x(-4 + x)) = 36 (-20 + 5x + (-4 * x + x * x)) = 36 (-20 + 5x + (-4x + x2)) = 36 Combine like terms: 5x + -4x = 1x (-20 + 1x + x2) = 36 Solving -20 + 1x + x2 = 36 Solving for variable 'x'. Reorder the terms: -20 + -36 + 1x + x2 = 36 + -36 Combine like terms: -20 + -36 = -56 -56 + 1x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -56 + 1x + x2 = 0 Factor a trinomial. (-8 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-8, 7}
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