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Simplifying (2x + -3)(-1x + 4) = (2x + -3)(3x + 8) Reorder the terms: (-3 + 2x)(-1x + 4) = (2x + -3)(3x + 8) Reorder the terms: (-3 + 2x)(4 + -1x) = (2x + -3)(3x + 8) Multiply (-3 + 2x) * (4 + -1x) (-3(4 + -1x) + 2x * (4 + -1x)) = (2x + -3)(3x + 8) ((4 * -3 + -1x * -3) + 2x * (4 + -1x)) = (2x + -3)(3x + 8) ((-12 + 3x) + 2x * (4 + -1x)) = (2x + -3)(3x + 8) (-12 + 3x + (4 * 2x + -1x * 2x)) = (2x + -3)(3x + 8) (-12 + 3x + (8x + -2x2)) = (2x + -3)(3x + 8) Combine like terms: 3x + 8x = 11x (-12 + 11x + -2x2) = (2x + -3)(3x + 8) Reorder the terms: -12 + 11x + -2x2 = (-3 + 2x)(3x + 8) Reorder the terms: -12 + 11x + -2x2 = (-3 + 2x)(8 + 3x) Multiply (-3 + 2x) * (8 + 3x) -12 + 11x + -2x2 = (-3(8 + 3x) + 2x * (8 + 3x)) -12 + 11x + -2x2 = ((8 * -3 + 3x * -3) + 2x * (8 + 3x)) -12 + 11x + -2x2 = ((-24 + -9x) + 2x * (8 + 3x)) -12 + 11x + -2x2 = (-24 + -9x + (8 * 2x + 3x * 2x)) -12 + 11x + -2x2 = (-24 + -9x + (16x + 6x2)) Combine like terms: -9x + 16x = 7x -12 + 11x + -2x2 = (-24 + 7x + 6x2) Solving -12 + 11x + -2x2 = -24 + 7x + 6x2 Solving for variable 'x'. Reorder the terms: -12 + 24 + 11x + -7x + -2x2 + -6x2 = -24 + 7x + 6x2 + 24 + -7x + -6x2 Combine like terms: -12 + 24 = 12 12 + 11x + -7x + -2x2 + -6x2 = -24 + 7x + 6x2 + 24 + -7x + -6x2 Combine like terms: 11x + -7x = 4x 12 + 4x + -2x2 + -6x2 = -24 + 7x + 6x2 + 24 + -7x + -6x2 Combine like terms: -2x2 + -6x2 = -8x2 12 + 4x + -8x2 = -24 + 7x + 6x2 + 24 + -7x + -6x2 Reorder the terms: 12 + 4x + -8x2 = -24 + 24 + 7x + -7x + 6x2 + -6x2 Combine like terms: -24 + 24 = 0 12 + 4x + -8x2 = 0 + 7x + -7x + 6x2 + -6x2 12 + 4x + -8x2 = 7x + -7x + 6x2 + -6x2 Combine like terms: 7x + -7x = 0 12 + 4x + -8x2 = 0 + 6x2 + -6x2 12 + 4x + -8x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 12 + 4x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + x + -2x2) = 0 Factor a trinomial. 4((3 + -2x)(1 + x)) = 0 Ignore the factor 4.Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {1.5, -1}
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