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Simplifying (x + 5)(x + 1) + -32 = 0 Reorder the terms: (5 + x)(x + 1) + -32 = 0 Reorder the terms: (5 + x)(1 + x) + -32 = 0 Multiply (5 + x) * (1 + x) (5(1 + x) + x(1 + x)) + -32 = 0 ((1 * 5 + x * 5) + x(1 + x)) + -32 = 0 ((5 + 5x) + x(1 + x)) + -32 = 0 (5 + 5x + (1 * x + x * x)) + -32 = 0 (5 + 5x + (1x + x2)) + -32 = 0 Combine like terms: 5x + 1x = 6x (5 + 6x + x2) + -32 = 0 Reorder the terms: 5 + -32 + 6x + x2 = 0 Combine like terms: 5 + -32 = -27 -27 + 6x + x2 = 0 Solving -27 + 6x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (-9 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-9, 3}
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