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Simplifying (4x + -5)(x + 4) = (x + 1)(5x + -4) Reorder the terms: (-5 + 4x)(x + 4) = (x + 1)(5x + -4) Reorder the terms: (-5 + 4x)(4 + x) = (x + 1)(5x + -4) Multiply (-5 + 4x) * (4 + x) (-5(4 + x) + 4x * (4 + x)) = (x + 1)(5x + -4) ((4 * -5 + x * -5) + 4x * (4 + x)) = (x + 1)(5x + -4) ((-20 + -5x) + 4x * (4 + x)) = (x + 1)(5x + -4) (-20 + -5x + (4 * 4x + x * 4x)) = (x + 1)(5x + -4) (-20 + -5x + (16x + 4x2)) = (x + 1)(5x + -4) Combine like terms: -5x + 16x = 11x (-20 + 11x + 4x2) = (x + 1)(5x + -4) Reorder the terms: -20 + 11x + 4x2 = (1 + x)(5x + -4) Reorder the terms: -20 + 11x + 4x2 = (1 + x)(-4 + 5x) Multiply (1 + x) * (-4 + 5x) -20 + 11x + 4x2 = (1(-4 + 5x) + x(-4 + 5x)) -20 + 11x + 4x2 = ((-4 * 1 + 5x * 1) + x(-4 + 5x)) -20 + 11x + 4x2 = ((-4 + 5x) + x(-4 + 5x)) -20 + 11x + 4x2 = (-4 + 5x + (-4 * x + 5x * x)) -20 + 11x + 4x2 = (-4 + 5x + (-4x + 5x2)) Combine like terms: 5x + -4x = 1x -20 + 11x + 4x2 = (-4 + 1x + 5x2) Solving -20 + 11x + 4x2 = -4 + 1x + 5x2 Solving for variable 'x'. Reorder the terms: -20 + 4 + 11x + -1x + 4x2 + -5x2 = -4 + 1x + 5x2 + 4 + -1x + -5x2 Combine like terms: -20 + 4 = -16 -16 + 11x + -1x + 4x2 + -5x2 = -4 + 1x + 5x2 + 4 + -1x + -5x2 Combine like terms: 11x + -1x = 10x -16 + 10x + 4x2 + -5x2 = -4 + 1x + 5x2 + 4 + -1x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -16 + 10x + -1x2 = -4 + 1x + 5x2 + 4 + -1x + -5x2 Reorder the terms: -16 + 10x + -1x2 = -4 + 4 + 1x + -1x + 5x2 + -5x2 Combine like terms: -4 + 4 = 0 -16 + 10x + -1x2 = 0 + 1x + -1x + 5x2 + -5x2 -16 + 10x + -1x2 = 1x + -1x + 5x2 + -5x2 Combine like terms: 1x + -1x = 0 -16 + 10x + -1x2 = 0 + 5x2 + -5x2 -16 + 10x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -16 + 10x + -1x2 = 0 Factor a trinomial. (-8 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
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 = 2Solution
x = {8, 2}
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