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Simplifying 3x(x + 20) + 12(x + 20) = 0 Reorder the terms: 3x(20 + x) + 12(x + 20) = 0 (20 * 3x + x * 3x) + 12(x + 20) = 0 (60x + 3x2) + 12(x + 20) = 0 Reorder the terms: 60x + 3x2 + 12(20 + x) = 0 60x + 3x2 + (20 * 12 + x * 12) = 0 60x + 3x2 + (240 + 12x) = 0 Reorder the terms: 240 + 60x + 12x + 3x2 = 0 Combine like terms: 60x + 12x = 72x 240 + 72x + 3x2 = 0 Solving 240 + 72x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(80 + 24x + x2) = 0 Factor a trinomial. 3((20 + x)(4 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20Subproblem 2
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 = -4Solution
x = {-20, -4}
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