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Simplifying (2x + 3) * x(x + -1) + -1(2x + 3) * x(x + 4) = 0 Reorder the terms: (3 + 2x) * x(x + -1) + -1(2x + 3) * x(x + 4) = 0 Reorder the terms: (3 + 2x) * x(-1 + x) + -1(2x + 3) * x(x + 4) = 0 Reorder the terms for easier multiplication: x(3 + 2x)(-1 + x) + -1(2x + 3) * x(x + 4) = 0 Multiply (3 + 2x) * (-1 + x) x(3(-1 + x) + 2x * (-1 + x)) + -1(2x + 3) * x(x + 4) = 0 x((-1 * 3 + x * 3) + 2x * (-1 + x)) + -1(2x + 3) * x(x + 4) = 0 x((-3 + 3x) + 2x * (-1 + x)) + -1(2x + 3) * x(x + 4) = 0 x(-3 + 3x + (-1 * 2x + x * 2x)) + -1(2x + 3) * x(x + 4) = 0 x(-3 + 3x + (-2x + 2x2)) + -1(2x + 3) * x(x + 4) = 0 Combine like terms: 3x + -2x = 1x x(-3 + 1x + 2x2) + -1(2x + 3) * x(x + 4) = 0 (-3 * x + 1x * x + 2x2 * x) + -1(2x + 3) * x(x + 4) = 0 (-3x + 1x2 + 2x3) + -1(2x + 3) * x(x + 4) = 0 Reorder the terms: -3x + 1x2 + 2x3 + -1(3 + 2x) * x(x + 4) = 0 Reorder the terms: -3x + 1x2 + 2x3 + -1(3 + 2x) * x(4 + x) = 0 Reorder the terms for easier multiplication: -3x + 1x2 + 2x3 + -1x(3 + 2x)(4 + x) = 0 Multiply (3 + 2x) * (4 + x) -3x + 1x2 + 2x3 + -1x(3(4 + x) + 2x * (4 + x)) = 0 -3x + 1x2 + 2x3 + -1x((4 * 3 + x * 3) + 2x * (4 + x)) = 0 -3x + 1x2 + 2x3 + -1x((12 + 3x) + 2x * (4 + x)) = 0 -3x + 1x2 + 2x3 + -1x(12 + 3x + (4 * 2x + x * 2x)) = 0 -3x + 1x2 + 2x3 + -1x(12 + 3x + (8x + 2x2)) = 0 Combine like terms: 3x + 8x = 11x -3x + 1x2 + 2x3 + -1x(12 + 11x + 2x2) = 0 -3x + 1x2 + 2x3 + (12 * -1x + 11x * -1x + 2x2 * -1x) = 0 -3x + 1x2 + 2x3 + (-12x + -11x2 + -2x3) = 0 Reorder the terms: -3x + -12x + 1x2 + -11x2 + 2x3 + -2x3 = 0 Combine like terms: -3x + -12x = -15x -15x + 1x2 + -11x2 + 2x3 + -2x3 = 0 Combine like terms: 1x2 + -11x2 = -10x2 -15x + -10x2 + 2x3 + -2x3 = 0 Combine like terms: 2x3 + -2x3 = 0 -15x + -10x2 + 0 = 0 -15x + -10x2 = 0 Solving -15x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-5x'. -5x(3 + 2x) = 0 Ignore the factor -5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = {0, -1.5}
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