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Simplifying (4x + -1)(2x + 3) = (3x + 3)(x + -1) Reorder the terms: (-1 + 4x)(2x + 3) = (3x + 3)(x + -1) Reorder the terms: (-1 + 4x)(3 + 2x) = (3x + 3)(x + -1) Multiply (-1 + 4x) * (3 + 2x) (-1(3 + 2x) + 4x * (3 + 2x)) = (3x + 3)(x + -1) ((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = (3x + 3)(x + -1) ((-3 + -2x) + 4x * (3 + 2x)) = (3x + 3)(x + -1) (-3 + -2x + (3 * 4x + 2x * 4x)) = (3x + 3)(x + -1) (-3 + -2x + (12x + 8x2)) = (3x + 3)(x + -1) Combine like terms: -2x + 12x = 10x (-3 + 10x + 8x2) = (3x + 3)(x + -1) Reorder the terms: -3 + 10x + 8x2 = (3 + 3x)(x + -1) Reorder the terms: -3 + 10x + 8x2 = (3 + 3x)(-1 + x) Multiply (3 + 3x) * (-1 + x) -3 + 10x + 8x2 = (3(-1 + x) + 3x * (-1 + x)) -3 + 10x + 8x2 = ((-1 * 3 + x * 3) + 3x * (-1 + x)) -3 + 10x + 8x2 = ((-3 + 3x) + 3x * (-1 + x)) -3 + 10x + 8x2 = (-3 + 3x + (-1 * 3x + x * 3x)) -3 + 10x + 8x2 = (-3 + 3x + (-3x + 3x2)) Combine like terms: 3x + -3x = 0 -3 + 10x + 8x2 = (-3 + 0 + 3x2) -3 + 10x + 8x2 = (-3 + 3x2) Add '3' to each side of the equation. -3 + 10x + 3 + 8x2 = -3 + 3 + 3x2 Reorder the terms: -3 + 3 + 10x + 8x2 = -3 + 3 + 3x2 Combine like terms: -3 + 3 = 0 0 + 10x + 8x2 = -3 + 3 + 3x2 10x + 8x2 = -3 + 3 + 3x2 Combine like terms: -3 + 3 = 0 10x + 8x2 = 0 + 3x2 10x + 8x2 = 3x2 Solving 10x + 8x2 = 3x2 Solving for variable 'x'. Combine like terms: 8x2 + -3x2 = 5x2 10x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(2 + x) = 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 '(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 = {0, -2}
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