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Simplifying (x + -2)(x + 9) = 5(x + 6) Reorder the terms: (-2 + x)(x + 9) = 5(x + 6) Reorder the terms: (-2 + x)(9 + x) = 5(x + 6) Multiply (-2 + x) * (9 + x) (-2(9 + x) + x(9 + x)) = 5(x + 6) ((9 * -2 + x * -2) + x(9 + x)) = 5(x + 6) ((-18 + -2x) + x(9 + x)) = 5(x + 6) (-18 + -2x + (9 * x + x * x)) = 5(x + 6) (-18 + -2x + (9x + x2)) = 5(x + 6) Combine like terms: -2x + 9x = 7x (-18 + 7x + x2) = 5(x + 6) Reorder the terms: -18 + 7x + x2 = 5(6 + x) -18 + 7x + x2 = (6 * 5 + x * 5) -18 + 7x + x2 = (30 + 5x) Solving -18 + 7x + x2 = 30 + 5x Solving for variable 'x'. Reorder the terms: -18 + -30 + 7x + -5x + x2 = 30 + 5x + -30 + -5x Combine like terms: -18 + -30 = -48 -48 + 7x + -5x + x2 = 30 + 5x + -30 + -5x Combine like terms: 7x + -5x = 2x -48 + 2x + x2 = 30 + 5x + -30 + -5x Reorder the terms: -48 + 2x + x2 = 30 + -30 + 5x + -5x Combine like terms: 30 + -30 = 0 -48 + 2x + x2 = 0 + 5x + -5x -48 + 2x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -48 + 2x + x2 = 0 Factor a trinomial. (-8 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-8, 6}
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