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Simplifying (x + 4)(x + -3) + -14 = (1 + -1x)(x + -2) Reorder the terms: (4 + x)(x + -3) + -14 = (1 + -1x)(x + -2) Reorder the terms: (4 + x)(-3 + x) + -14 = (1 + -1x)(x + -2) Multiply (4 + x) * (-3 + x) (4(-3 + x) + x(-3 + x)) + -14 = (1 + -1x)(x + -2) ((-3 * 4 + x * 4) + x(-3 + x)) + -14 = (1 + -1x)(x + -2) ((-12 + 4x) + x(-3 + x)) + -14 = (1 + -1x)(x + -2) (-12 + 4x + (-3 * x + x * x)) + -14 = (1 + -1x)(x + -2) (-12 + 4x + (-3x + x2)) + -14 = (1 + -1x)(x + -2) Combine like terms: 4x + -3x = 1x (-12 + 1x + x2) + -14 = (1 + -1x)(x + -2) Reorder the terms: -12 + -14 + 1x + x2 = (1 + -1x)(x + -2) Combine like terms: -12 + -14 = -26 -26 + 1x + x2 = (1 + -1x)(x + -2) Reorder the terms: -26 + 1x + x2 = (1 + -1x)(-2 + x) Multiply (1 + -1x) * (-2 + x) -26 + 1x + x2 = (1(-2 + x) + -1x * (-2 + x)) -26 + 1x + x2 = ((-2 * 1 + x * 1) + -1x * (-2 + x)) -26 + 1x + x2 = ((-2 + 1x) + -1x * (-2 + x)) -26 + 1x + x2 = (-2 + 1x + (-2 * -1x + x * -1x)) -26 + 1x + x2 = (-2 + 1x + (2x + -1x2)) Combine like terms: 1x + 2x = 3x -26 + 1x + x2 = (-2 + 3x + -1x2) Solving -26 + 1x + x2 = -2 + 3x + -1x2 Solving for variable 'x'. Reorder the terms: -26 + 2 + 1x + -3x + x2 + x2 = -2 + 3x + -1x2 + 2 + -3x + x2 Combine like terms: -26 + 2 = -24 -24 + 1x + -3x + x2 + x2 = -2 + 3x + -1x2 + 2 + -3x + x2 Combine like terms: 1x + -3x = -2x -24 + -2x + x2 + x2 = -2 + 3x + -1x2 + 2 + -3x + x2 Combine like terms: x2 + x2 = 2x2 -24 + -2x + 2x2 = -2 + 3x + -1x2 + 2 + -3x + x2 Reorder the terms: -24 + -2x + 2x2 = -2 + 2 + 3x + -3x + -1x2 + x2 Combine like terms: -2 + 2 = 0 -24 + -2x + 2x2 = 0 + 3x + -3x + -1x2 + x2 -24 + -2x + 2x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -24 + -2x + 2x2 = 0 + -1x2 + x2 -24 + -2x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -24 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -1x + x2) = 0 Factor a trinomial. 2((-3 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-3, 4}
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