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Simplifying (2x + 3)(-1x) + -1(-1x) = (2)(2)(2x + 3) Reorder the terms: (3 + 2x)(-1x) + -1(-1x) = (2)(2)(2x + 3) Remove parenthesis around (-1x) (3 + 2x) * -1x + -1(-1x) = (2)(2)(2x + 3) Reorder the terms for easier multiplication: -1x(3 + 2x) + -1(-1x) = (2)(2)(2x + 3) (3 * -1x + 2x * -1x) + -1(-1x) = (2)(2)(2x + 3) (-3x + -2x2) + -1(-1x) = (2)(2)(2x + 3) Remove parenthesis around (-1x) -3x + -2x2 + -1 * -1x = (2)(2)(2x + 3) Multiply -1 * -1 -3x + -2x2 + 1x = (2)(2)(2x + 3) Reorder the terms: -3x + 1x + -2x2 = (2)(2)(2x + 3) Combine like terms: -3x + 1x = -2x -2x + -2x2 = (2)(2)(2x + 3) Reorder the terms: -2x + -2x2 = 2 * 2(3 + 2x) Multiply 2 * 2 -2x + -2x2 = 4(3 + 2x) -2x + -2x2 = (3 * 4 + 2x * 4) -2x + -2x2 = (12 + 8x) Solving -2x + -2x2 = 12 + 8x Solving for variable 'x'. Reorder the terms: -12 + -2x + -8x + -2x2 = 12 + 8x + -12 + -8x Combine like terms: -2x + -8x = -10x -12 + -10x + -2x2 = 12 + 8x + -12 + -8x Reorder the terms: -12 + -10x + -2x2 = 12 + -12 + 8x + -8x Combine like terms: 12 + -12 = 0 -12 + -10x + -2x2 = 0 + 8x + -8x -12 + -10x + -2x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -12 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 5x + x2) = 0 Factor a trinomial. -2((3 + x)(2 + x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 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 = {-3, -2}
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