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Simplifying (2x + -3) + -1(2x + -3)(x + 1) + -2(2x + -3) = 0 Reorder the terms: (-3 + 2x) + -1(2x + -3)(x + 1) + -2(2x + -3) = 0 Remove parenthesis around (-3 + 2x) -3 + 2x + -1(2x + -3)(x + 1) + -2(2x + -3) = 0 Reorder the terms: -3 + 2x + -1(-3 + 2x)(x + 1) + -2(2x + -3) = 0 Reorder the terms: -3 + 2x + -1(-3 + 2x)(1 + x) + -2(2x + -3) = 0 Multiply (-3 + 2x) * (1 + x) -3 + 2x + -1(-3(1 + x) + 2x * (1 + x)) + -2(2x + -3) = 0 -3 + 2x + -1((1 * -3 + x * -3) + 2x * (1 + x)) + -2(2x + -3) = 0 -3 + 2x + -1((-3 + -3x) + 2x * (1 + x)) + -2(2x + -3) = 0 -3 + 2x + -1(-3 + -3x + (1 * 2x + x * 2x)) + -2(2x + -3) = 0 -3 + 2x + -1(-3 + -3x + (2x + 2x2)) + -2(2x + -3) = 0 Combine like terms: -3x + 2x = -1x -3 + 2x + -1(-3 + -1x + 2x2) + -2(2x + -3) = 0 -3 + 2x + (-3 * -1 + -1x * -1 + 2x2 * -1) + -2(2x + -3) = 0 -3 + 2x + (3 + 1x + -2x2) + -2(2x + -3) = 0 Reorder the terms: -3 + 2x + 3 + 1x + -2x2 + -2(-3 + 2x) = 0 -3 + 2x + 3 + 1x + -2x2 + (-3 * -2 + 2x * -2) = 0 -3 + 2x + 3 + 1x + -2x2 + (6 + -4x) = 0 Reorder the terms: -3 + 3 + 6 + 2x + 1x + -4x + -2x2 = 0 Combine like terms: -3 + 3 = 0 0 + 6 + 2x + 1x + -4x + -2x2 = 0 6 + 2x + 1x + -4x + -2x2 = 0 Combine like terms: 2x + 1x = 3x 6 + 3x + -4x + -2x2 = 0 Combine like terms: 3x + -4x = -1x 6 + -1x + -2x2 = 0 Solving 6 + -1x + -2x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -2x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {1.5, -2}
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