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Simplifying (x + -6)(x + 2) = 9 Reorder the terms: (-6 + x)(x + 2) = 9 Reorder the terms: (-6 + x)(2 + x) = 9 Multiply (-6 + x) * (2 + x) (-6(2 + x) + x(2 + x)) = 9 ((2 * -6 + x * -6) + x(2 + x)) = 9 ((-12 + -6x) + x(2 + x)) = 9 (-12 + -6x + (2 * x + x * x)) = 9 (-12 + -6x + (2x + x2)) = 9 Combine like terms: -6x + 2x = -4x (-12 + -4x + x2) = 9 Solving -12 + -4x + x2 = 9 Solving for variable 'x'. Reorder the terms: -12 + -9 + -4x + x2 = 9 + -9 Combine like terms: -12 + -9 = -21 -21 + -4x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -21 + -4x + x2 = 0 Factor a trinomial. (-3 + -1x)(7 + -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 '(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 = {-3, 7}
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