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Simplifying 14q3 + 32q2 + -30q = 0 Reorder the terms: -30q + 32q2 + 14q3 = 0 Solving -30q + 32q2 + 14q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2q'. 2q(-15 + 16q + 7q2) = 0 Factor a trinomial. 2q((-3 + -1q)(5 + -7q)) = 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 '(-3 + -1q)' equal to zero and attempt to solve: Simplifying -3 + -1q = 0 Solving -3 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1q = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1q = 0 + 3 -1q = 0 + 3 Combine like terms: 0 + 3 = 3 -1q = 3 Divide each side by '-1'. q = -3 Simplifying q = -3Subproblem 3
Set the factor '(5 + -7q)' equal to zero and attempt to solve: Simplifying 5 + -7q = 0 Solving 5 + -7q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7q = 0 + -5 -7q = 0 + -5 Combine like terms: 0 + -5 = -5 -7q = -5 Divide each side by '-7'. q = 0.7142857143 Simplifying q = 0.7142857143Solution
q = {0, -3, 0.7142857143}
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