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Simplifying (x + -2)(x + 3) = 24 Reorder the terms: (-2 + x)(x + 3) = 24 Reorder the terms: (-2 + x)(3 + x) = 24 Multiply (-2 + x) * (3 + x) (-2(3 + x) + x(3 + x)) = 24 ((3 * -2 + x * -2) + x(3 + x)) = 24 ((-6 + -2x) + x(3 + x)) = 24 (-6 + -2x + (3 * x + x * x)) = 24 (-6 + -2x + (3x + x2)) = 24 Combine like terms: -2x + 3x = 1x (-6 + 1x + x2) = 24 Solving -6 + 1x + x2 = 24 Solving for variable 'x'. Reorder the terms: -6 + -24 + 1x + x2 = 24 + -24 Combine like terms: -6 + -24 = -30 -30 + 1x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -30 + 1x + x2 = 0 Factor a trinomial. (-6 + -1x)(5 + -1x) = 0Subproblem 1
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 = -6Subproblem 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 = {-6, 5}
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