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Simplifying (x + 2)(-1x + 1) = (x + 2)(3x + 4) Reorder the terms: (2 + x)(-1x + 1) = (x + 2)(3x + 4) Reorder the terms: (2 + x)(1 + -1x) = (x + 2)(3x + 4) Multiply (2 + x) * (1 + -1x) (2(1 + -1x) + x(1 + -1x)) = (x + 2)(3x + 4) ((1 * 2 + -1x * 2) + x(1 + -1x)) = (x + 2)(3x + 4) ((2 + -2x) + x(1 + -1x)) = (x + 2)(3x + 4) (2 + -2x + (1 * x + -1x * x)) = (x + 2)(3x + 4) (2 + -2x + (1x + -1x2)) = (x + 2)(3x + 4) Combine like terms: -2x + 1x = -1x (2 + -1x + -1x2) = (x + 2)(3x + 4) Reorder the terms: 2 + -1x + -1x2 = (2 + x)(3x + 4) Reorder the terms: 2 + -1x + -1x2 = (2 + x)(4 + 3x) Multiply (2 + x) * (4 + 3x) 2 + -1x + -1x2 = (2(4 + 3x) + x(4 + 3x)) 2 + -1x + -1x2 = ((4 * 2 + 3x * 2) + x(4 + 3x)) 2 + -1x + -1x2 = ((8 + 6x) + x(4 + 3x)) 2 + -1x + -1x2 = (8 + 6x + (4 * x + 3x * x)) 2 + -1x + -1x2 = (8 + 6x + (4x + 3x2)) Combine like terms: 6x + 4x = 10x 2 + -1x + -1x2 = (8 + 10x + 3x2) Solving 2 + -1x + -1x2 = 8 + 10x + 3x2 Solving for variable 'x'. Reorder the terms: 2 + -8 + -1x + -10x + -1x2 + -3x2 = 8 + 10x + 3x2 + -8 + -10x + -3x2 Combine like terms: 2 + -8 = -6 -6 + -1x + -10x + -1x2 + -3x2 = 8 + 10x + 3x2 + -8 + -10x + -3x2 Combine like terms: -1x + -10x = -11x -6 + -11x + -1x2 + -3x2 = 8 + 10x + 3x2 + -8 + -10x + -3x2 Combine like terms: -1x2 + -3x2 = -4x2 -6 + -11x + -4x2 = 8 + 10x + 3x2 + -8 + -10x + -3x2 Reorder the terms: -6 + -11x + -4x2 = 8 + -8 + 10x + -10x + 3x2 + -3x2 Combine like terms: 8 + -8 = 0 -6 + -11x + -4x2 = 0 + 10x + -10x + 3x2 + -3x2 -6 + -11x + -4x2 = 10x + -10x + 3x2 + -3x2 Combine like terms: 10x + -10x = 0 -6 + -11x + -4x2 = 0 + 3x2 + -3x2 -6 + -11x + -4x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + -11x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 11x + 4x2) = 0 Factor a trinomial. -1((2 + x)(3 + 4x)) = 0 Ignore the factor -1.Subproblem 1
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 = -2Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-2, -0.75}
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