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Simplifying 5x(x + 4) = -75 + -20x Reorder the terms: 5x(4 + x) = -75 + -20x (4 * 5x + x * 5x) = -75 + -20x (20x + 5x2) = -75 + -20x Solving 20x + 5x2 = -75 + -20x Solving for variable 'x'. Reorder the terms: 75 + 20x + 20x + 5x2 = -75 + -20x + 75 + 20x Combine like terms: 20x + 20x = 40x 75 + 40x + 5x2 = -75 + -20x + 75 + 20x Reorder the terms: 75 + 40x + 5x2 = -75 + 75 + -20x + 20x Combine like terms: -75 + 75 = 0 75 + 40x + 5x2 = 0 + -20x + 20x 75 + 40x + 5x2 = -20x + 20x Combine like terms: -20x + 20x = 0 75 + 40x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(15 + 8x + x2) = 0 Factor a trinomial. 5((5 + x)(3 + x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-5, -3}
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