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Simplifying 0 = 24q2 + -8q Reorder the terms: 0 = -8q + 24q2 Solving 0 = -8q + 24q2 Solving for variable 'q'. Remove the zero: 8q + -24q2 = -8q + 24q2 + 8q + -24q2 Reorder the terms: 8q + -24q2 = -8q + 8q + 24q2 + -24q2 Combine like terms: -8q + 8q = 0 8q + -24q2 = 0 + 24q2 + -24q2 8q + -24q2 = 24q2 + -24q2 Combine like terms: 24q2 + -24q2 = 0 8q + -24q2 = 0 Factor out the Greatest Common Factor (GCF), '8q'. 8q(1 + -3q) = 0 Ignore the factor 8.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 + -3q)' equal to zero and attempt to solve: Simplifying 1 + -3q = 0 Solving 1 + -3q = 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 + -3q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3q = 0 + -1 -3q = 0 + -1 Combine like terms: 0 + -1 = -1 -3q = -1 Divide each side by '-3'. q = 0.3333333333 Simplifying q = 0.3333333333Solution
q = {0, 0.3333333333}
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