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Simplifying (3x + -2)(x + 1) + -1(x + 1)(x + 4) = 0 Reorder the terms: (-2 + 3x)(x + 1) + -1(x + 1)(x + 4) = 0 Reorder the terms: (-2 + 3x)(1 + x) + -1(x + 1)(x + 4) = 0 Multiply (-2 + 3x) * (1 + x) (-2(1 + x) + 3x * (1 + x)) + -1(x + 1)(x + 4) = 0 ((1 * -2 + x * -2) + 3x * (1 + x)) + -1(x + 1)(x + 4) = 0 ((-2 + -2x) + 3x * (1 + x)) + -1(x + 1)(x + 4) = 0 (-2 + -2x + (1 * 3x + x * 3x)) + -1(x + 1)(x + 4) = 0 (-2 + -2x + (3x + 3x2)) + -1(x + 1)(x + 4) = 0 Combine like terms: -2x + 3x = 1x (-2 + 1x + 3x2) + -1(x + 1)(x + 4) = 0 Reorder the terms: -2 + 1x + 3x2 + -1(1 + x)(x + 4) = 0 Reorder the terms: -2 + 1x + 3x2 + -1(1 + x)(4 + x) = 0 Multiply (1 + x) * (4 + x) -2 + 1x + 3x2 + -1(1(4 + x) + x(4 + x)) = 0 -2 + 1x + 3x2 + -1((4 * 1 + x * 1) + x(4 + x)) = 0 -2 + 1x + 3x2 + -1((4 + 1x) + x(4 + x)) = 0 -2 + 1x + 3x2 + -1(4 + 1x + (4 * x + x * x)) = 0 -2 + 1x + 3x2 + -1(4 + 1x + (4x + x2)) = 0 Combine like terms: 1x + 4x = 5x -2 + 1x + 3x2 + -1(4 + 5x + x2) = 0 -2 + 1x + 3x2 + (4 * -1 + 5x * -1 + x2 * -1) = 0 -2 + 1x + 3x2 + (-4 + -5x + -1x2) = 0 Reorder the terms: -2 + -4 + 1x + -5x + 3x2 + -1x2 = 0 Combine like terms: -2 + -4 = -6 -6 + 1x + -5x + 3x2 + -1x2 = 0 Combine like terms: 1x + -5x = -4x -6 + -4x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -6 + -4x + 2x2 = 0 Solving -6 + -4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -2x + x2) = 0 Factor a trinomial. 2((-1 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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, 3}
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