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Simplifying (x + 4)(2x + -1) = (-1x + -7)(4 + x) Reorder the terms: (4 + x)(2x + -1) = (-1x + -7)(4 + x) Reorder the terms: (4 + x)(-1 + 2x) = (-1x + -7)(4 + x) Multiply (4 + x) * (-1 + 2x) (4(-1 + 2x) + x(-1 + 2x)) = (-1x + -7)(4 + x) ((-1 * 4 + 2x * 4) + x(-1 + 2x)) = (-1x + -7)(4 + x) ((-4 + 8x) + x(-1 + 2x)) = (-1x + -7)(4 + x) (-4 + 8x + (-1 * x + 2x * x)) = (-1x + -7)(4 + x) (-4 + 8x + (-1x + 2x2)) = (-1x + -7)(4 + x) Combine like terms: 8x + -1x = 7x (-4 + 7x + 2x2) = (-1x + -7)(4 + x) Reorder the terms: -4 + 7x + 2x2 = (-7 + -1x)(4 + x) Multiply (-7 + -1x) * (4 + x) -4 + 7x + 2x2 = (-7(4 + x) + -1x * (4 + x)) -4 + 7x + 2x2 = ((4 * -7 + x * -7) + -1x * (4 + x)) -4 + 7x + 2x2 = ((-28 + -7x) + -1x * (4 + x)) -4 + 7x + 2x2 = (-28 + -7x + (4 * -1x + x * -1x)) -4 + 7x + 2x2 = (-28 + -7x + (-4x + -1x2)) Combine like terms: -7x + -4x = -11x -4 + 7x + 2x2 = (-28 + -11x + -1x2) Solving -4 + 7x + 2x2 = -28 + -11x + -1x2 Solving for variable 'x'. Reorder the terms: -4 + 28 + 7x + 11x + 2x2 + x2 = -28 + -11x + -1x2 + 28 + 11x + x2 Combine like terms: -4 + 28 = 24 24 + 7x + 11x + 2x2 + x2 = -28 + -11x + -1x2 + 28 + 11x + x2 Combine like terms: 7x + 11x = 18x 24 + 18x + 2x2 + x2 = -28 + -11x + -1x2 + 28 + 11x + x2 Combine like terms: 2x2 + x2 = 3x2 24 + 18x + 3x2 = -28 + -11x + -1x2 + 28 + 11x + x2 Reorder the terms: 24 + 18x + 3x2 = -28 + 28 + -11x + 11x + -1x2 + x2 Combine like terms: -28 + 28 = 0 24 + 18x + 3x2 = 0 + -11x + 11x + -1x2 + x2 24 + 18x + 3x2 = -11x + 11x + -1x2 + x2 Combine like terms: -11x + 11x = 0 24 + 18x + 3x2 = 0 + -1x2 + x2 24 + 18x + 3x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 24 + 18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 6x + x2) = 0 Factor a trinomial. 3((4 + x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 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 = {-4, -2}
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