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Simplifying 2q3 + -38q2 + 120q = 0 Reorder the terms: 120q + -38q2 + 2q3 = 0 Solving 120q + -38q2 + 2q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2q'. 2q(60 + -19q + q2) = 0 Factor a trinomial. 2q((4 + -1q)(15 + -1q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q = 0Subproblem 2
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 3
Set the factor '(15 + -1q)' equal to zero and attempt to solve: Simplifying 15 + -1q = 0 Solving 15 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1q = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1q = 0 + -15 -1q = 0 + -15 Combine like terms: 0 + -15 = -15 -1q = -15 Divide each side by '-1'. q = 15 Simplifying q = 15Solution
q = {0, 4, 15}
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