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Simplifying 3x(x + 6) = 120 Reorder the terms: 3x(6 + x) = 120 (6 * 3x + x * 3x) = 120 (18x + 3x2) = 120 Solving 18x + 3x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 18x + 3x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-40 + 6x + x2) = 0 Factor a trinomial. 3((-10 + -1x)(4 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 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 = {-10, 4}
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