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Simplifying (x + -2)(x + 6) = 9 Reorder the terms: (-2 + x)(x + 6) = 9 Reorder the terms: (-2 + x)(6 + x) = 9 Multiply (-2 + x) * (6 + x) (-2(6 + x) + x(6 + x)) = 9 ((6 * -2 + x * -2) + x(6 + x)) = 9 ((-12 + -2x) + x(6 + x)) = 9 (-12 + -2x + (6 * x + x * x)) = 9 (-12 + -2x + (6x + x2)) = 9 Combine like terms: -2x + 6x = 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. (-7 + -1x)(3 + -1x) = 0Subproblem 1
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 = -7Subproblem 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 = {-7, 3}
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