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Simplifying (x + 5)(5x + -4) = (x + -4)(1 + -3x) Reorder the terms: (5 + x)(5x + -4) = (x + -4)(1 + -3x) Reorder the terms: (5 + x)(-4 + 5x) = (x + -4)(1 + -3x) Multiply (5 + x) * (-4 + 5x) (5(-4 + 5x) + x(-4 + 5x)) = (x + -4)(1 + -3x) ((-4 * 5 + 5x * 5) + x(-4 + 5x)) = (x + -4)(1 + -3x) ((-20 + 25x) + x(-4 + 5x)) = (x + -4)(1 + -3x) (-20 + 25x + (-4 * x + 5x * x)) = (x + -4)(1 + -3x) (-20 + 25x + (-4x + 5x2)) = (x + -4)(1 + -3x) Combine like terms: 25x + -4x = 21x (-20 + 21x + 5x2) = (x + -4)(1 + -3x) Reorder the terms: -20 + 21x + 5x2 = (-4 + x)(1 + -3x) Multiply (-4 + x) * (1 + -3x) -20 + 21x + 5x2 = (-4(1 + -3x) + x(1 + -3x)) -20 + 21x + 5x2 = ((1 * -4 + -3x * -4) + x(1 + -3x)) -20 + 21x + 5x2 = ((-4 + 12x) + x(1 + -3x)) -20 + 21x + 5x2 = (-4 + 12x + (1 * x + -3x * x)) -20 + 21x + 5x2 = (-4 + 12x + (1x + -3x2)) Combine like terms: 12x + 1x = 13x -20 + 21x + 5x2 = (-4 + 13x + -3x2) Solving -20 + 21x + 5x2 = -4 + 13x + -3x2 Solving for variable 'x'. Reorder the terms: -20 + 4 + 21x + -13x + 5x2 + 3x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2 Combine like terms: -20 + 4 = -16 -16 + 21x + -13x + 5x2 + 3x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2 Combine like terms: 21x + -13x = 8x -16 + 8x + 5x2 + 3x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2 Combine like terms: 5x2 + 3x2 = 8x2 -16 + 8x + 8x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2 Reorder the terms: -16 + 8x + 8x2 = -4 + 4 + 13x + -13x + -3x2 + 3x2 Combine like terms: -4 + 4 = 0 -16 + 8x + 8x2 = 0 + 13x + -13x + -3x2 + 3x2 -16 + 8x + 8x2 = 13x + -13x + -3x2 + 3x2 Combine like terms: 13x + -13x = 0 -16 + 8x + 8x2 = 0 + -3x2 + 3x2 -16 + 8x + 8x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -16 + 8x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + x + x2) = 0 Factor a trinomial. 8((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 1Solution
x = {-2, 1}
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