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Simplifying (4x + 8)(5x + -20) = 0 Reorder the terms: (8 + 4x)(5x + -20) = 0 Reorder the terms: (8 + 4x)(-20 + 5x) = 0 Multiply (8 + 4x) * (-20 + 5x) (8(-20 + 5x) + 4x * (-20 + 5x)) = 0 ((-20 * 8 + 5x * 8) + 4x * (-20 + 5x)) = 0 ((-160 + 40x) + 4x * (-20 + 5x)) = 0 (-160 + 40x + (-20 * 4x + 5x * 4x)) = 0 (-160 + 40x + (-80x + 20x2)) = 0 Combine like terms: 40x + -80x = -40x (-160 + -40x + 20x2) = 0 Solving -160 + -40x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(-8 + -2x + x2) = 0 Factor a trinomial. 20((-2 + -1x)(4 + -1x)) = 0 Ignore the factor 20.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 '(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 = {-2, 4}
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