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Simplifying 7q3 + 31q2 + 12q = 0 Reorder the terms: 12q + 31q2 + 7q3 = 0 Solving 12q + 31q2 + 7q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(12 + 31q + 7q2) = 0 Factor a trinomial. q((4 + q)(3 + 7q)) = 0Subproblem 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 + q)' equal to zero and attempt to solve: Simplifying 4 + q = 0 Solving 4 + q = 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 + q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + q = 0 + -4 q = 0 + -4 Combine like terms: 0 + -4 = -4 q = -4 Simplifying q = -4Subproblem 3
Set the factor '(3 + 7q)' equal to zero and attempt to solve: Simplifying 3 + 7q = 0 Solving 3 + 7q = 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 + 7q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7q = 0 + -3 7q = 0 + -3 Combine like terms: 0 + -3 = -3 7q = -3 Divide each side by '7'. q = -0.4285714286 Simplifying q = -0.4285714286Solution
q = {0, -4, -0.4285714286}
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