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Simplifying (2x + -3)(x + 2) = 9 Reorder the terms: (-3 + 2x)(x + 2) = 9 Reorder the terms: (-3 + 2x)(2 + x) = 9 Multiply (-3 + 2x) * (2 + x) (-3(2 + x) + 2x * (2 + x)) = 9 ((2 * -3 + x * -3) + 2x * (2 + x)) = 9 ((-6 + -3x) + 2x * (2 + x)) = 9 (-6 + -3x + (2 * 2x + x * 2x)) = 9 (-6 + -3x + (4x + 2x2)) = 9 Combine like terms: -3x + 4x = 1x (-6 + 1x + 2x2) = 9 Solving -6 + 1x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -6 + -9 + 1x + 2x2 = 9 + -9 Combine like terms: -6 + -9 = -15 -15 + 1x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -15 + 1x + 2x2 = 0 Factor a trinomial. (-3 + -1x)(5 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-3, 2.5}
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