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Simplifying (x + -6)(x + 7) = 3(x + -9) Reorder the terms: (-6 + x)(x + 7) = 3(x + -9) Reorder the terms: (-6 + x)(7 + x) = 3(x + -9) Multiply (-6 + x) * (7 + x) (-6(7 + x) + x(7 + x)) = 3(x + -9) ((7 * -6 + x * -6) + x(7 + x)) = 3(x + -9) ((-42 + -6x) + x(7 + x)) = 3(x + -9) (-42 + -6x + (7 * x + x * x)) = 3(x + -9) (-42 + -6x + (7x + x2)) = 3(x + -9) Combine like terms: -6x + 7x = 1x (-42 + 1x + x2) = 3(x + -9) Reorder the terms: -42 + 1x + x2 = 3(-9 + x) -42 + 1x + x2 = (-9 * 3 + x * 3) -42 + 1x + x2 = (-27 + 3x) Solving -42 + 1x + x2 = -27 + 3x Solving for variable 'x'. Reorder the terms: -42 + 27 + 1x + -3x + x2 = -27 + 3x + 27 + -3x Combine like terms: -42 + 27 = -15 -15 + 1x + -3x + x2 = -27 + 3x + 27 + -3x Combine like terms: 1x + -3x = -2x -15 + -2x + x2 = -27 + 3x + 27 + -3x Reorder the terms: -15 + -2x + x2 = -27 + 27 + 3x + -3x Combine like terms: -27 + 27 = 0 -15 + -2x + x2 = 0 + 3x + -3x -15 + -2x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -15 + -2x + x2 = 0 Factor a trinomial. (-3 + -1x)(5 + -1x) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-3, 5}
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