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Simplifying (2x + -3)(x + 2) + -5(2x + -3) = 0 Reorder the terms: (-3 + 2x)(x + 2) + -5(2x + -3) = 0 Reorder the terms: (-3 + 2x)(2 + x) + -5(2x + -3) = 0 Multiply (-3 + 2x) * (2 + x) (-3(2 + x) + 2x * (2 + x)) + -5(2x + -3) = 0 ((2 * -3 + x * -3) + 2x * (2 + x)) + -5(2x + -3) = 0 ((-6 + -3x) + 2x * (2 + x)) + -5(2x + -3) = 0 (-6 + -3x + (2 * 2x + x * 2x)) + -5(2x + -3) = 0 (-6 + -3x + (4x + 2x2)) + -5(2x + -3) = 0 Combine like terms: -3x + 4x = 1x (-6 + 1x + 2x2) + -5(2x + -3) = 0 Reorder the terms: -6 + 1x + 2x2 + -5(-3 + 2x) = 0 -6 + 1x + 2x2 + (-3 * -5 + 2x * -5) = 0 -6 + 1x + 2x2 + (15 + -10x) = 0 Reorder the terms: -6 + 15 + 1x + -10x + 2x2 = 0 Combine like terms: -6 + 15 = 9 9 + 1x + -10x + 2x2 = 0 Combine like terms: 1x + -10x = -9x 9 + -9x + 2x2 = 0 Solving 9 + -9x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -2x)(3 + -1x) = 0Subproblem 1
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 = 1.5Subproblem 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 = {1.5, 3}
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