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Simplifying 3x(2x + -9) = -30 Reorder the terms: 3x(-9 + 2x) = -30 (-9 * 3x + 2x * 3x) = -30 (-27x + 6x2) = -30 Solving -27x + 6x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + -27x + 6x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + -27x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -9x + 2x2) = 0 Factor a trinomial. 3((2 + -1x)(5 + -2x)) = 0 Ignore the factor 3.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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {2, 2.5}
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