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Simplifying 0 = (58 + -12q) * q Reorder the terms for easier multiplication: 0 = q(58 + -12q) 0 = (58 * q + -12q * q) 0 = (58q + -12q2) Solving 0 = 58q + -12q2 Solving for variable 'q'. Remove the zero: -58q + 12q2 = 58q + -12q2 + -58q + 12q2 Reorder the terms: -58q + 12q2 = 58q + -58q + -12q2 + 12q2 Combine like terms: 58q + -58q = 0 -58q + 12q2 = 0 + -12q2 + 12q2 -58q + 12q2 = -12q2 + 12q2 Combine like terms: -12q2 + 12q2 = 0 -58q + 12q2 = 0 Factor out the Greatest Common Factor (GCF), '2q'. 2q(-29 + 6q) = 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 '(-29 + 6q)' equal to zero and attempt to solve: Simplifying -29 + 6q = 0 Solving -29 + 6q = 0 Move all terms containing q to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + 6q = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 6q = 0 + 29 6q = 0 + 29 Combine like terms: 0 + 29 = 29 6q = 29 Divide each side by '6'. q = 4.833333333 Simplifying q = 4.833333333Solution
q = {0, 4.833333333}
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