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Simplifying 6x(3x + 9) = 180 Reorder the terms: 6x(9 + 3x) = 180 (9 * 6x + 3x * 6x) = 180 (54x + 18x2) = 180 Solving 54x + 18x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 54x + 18x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 54x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '18'. 18(-10 + 3x + x2) = 0 Factor a trinomial. 18((-5 + -1x)(2 + -1x)) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 2}
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