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Simplifying (x + -1)(2x + 3) = 3 Reorder the terms: (-1 + x)(2x + 3) = 3 Reorder the terms: (-1 + x)(3 + 2x) = 3 Multiply (-1 + x) * (3 + 2x) (-1(3 + 2x) + x(3 + 2x)) = 3 ((3 * -1 + 2x * -1) + x(3 + 2x)) = 3 ((-3 + -2x) + x(3 + 2x)) = 3 (-3 + -2x + (3 * x + 2x * x)) = 3 (-3 + -2x + (3x + 2x2)) = 3 Combine like terms: -2x + 3x = 1x (-3 + 1x + 2x2) = 3 Solving -3 + 1x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -3 + 1x + 2x2 = 3 + -3 Combine like terms: -3 + -3 = -6 -6 + 1x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -6 + 1x + 2x2 = 0 Factor a trinomial. (-2 + -1x)(3 + -2x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-2, 1.5}
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