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Simplifying 6q3 + -16q2 + 10q = 0 Reorder the terms: 10q + -16q2 + 6q3 = 0 Solving 10q + -16q2 + 6q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2q'. 2q(5 + -8q + 3q2) = 0 Factor a trinomial. 2q((1 + -1q)(5 + -3q)) = 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 '(1 + -1q)' equal to zero and attempt to solve: Simplifying 1 + -1q = 0 Solving 1 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1q = 0 + -1 -1q = 0 + -1 Combine like terms: 0 + -1 = -1 -1q = -1 Divide each side by '-1'. q = 1 Simplifying q = 1Subproblem 3
Set the factor '(5 + -3q)' equal to zero and attempt to solve: Simplifying 5 + -3q = 0 Solving 5 + -3q = 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 + -3q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3q = 0 + -5 -3q = 0 + -5 Combine like terms: 0 + -5 = -5 -3q = -5 Divide each side by '-3'. q = 1.666666667 Simplifying q = 1.666666667Solution
q = {0, 1, 1.666666667}
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