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Simplifying 18q2 + 60q + -48 = 0 Reorder the terms: -48 + 60q + 18q2 = 0 Solving -48 + 60q + 18q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + 10q + 3q2) = 0 Factor a trinomial. 6((-4 + -1q)(2 + -3q)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -1q)' equal to zero and attempt to solve: Simplifying -4 + -1q = 0 Solving -4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1q = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1q = 0 + 4 -1q = 0 + 4 Combine like terms: 0 + 4 = 4 -1q = 4 Divide each side by '-1'. q = -4 Simplifying q = -4Subproblem 2
Set the factor '(2 + -3q)' equal to zero and attempt to solve: Simplifying 2 + -3q = 0 Solving 2 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3q = 0 + -2 -3q = 0 + -2 Combine like terms: 0 + -2 = -2 -3q = -2 Divide each side by '-3'. q = 0.6666666667 Simplifying q = 0.6666666667Solution
q = {-4, 0.6666666667}
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