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Simplifying 58 + -6q + q2 = 58 + -12q + 3q2 Add '-58' to each side of the equation. 58 + -6q + -58 + q2 = 58 + -12q + -58 + 3q2 Reorder the terms: 58 + -58 + -6q + q2 = 58 + -12q + -58 + 3q2 Combine like terms: 58 + -58 = 0 0 + -6q + q2 = 58 + -12q + -58 + 3q2 -6q + q2 = 58 + -12q + -58 + 3q2 Reorder the terms: -6q + q2 = 58 + -58 + -12q + 3q2 Combine like terms: 58 + -58 = 0 -6q + q2 = 0 + -12q + 3q2 -6q + q2 = -12q + 3q2 Solving -6q + q2 = -12q + 3q2 Solving for variable 'q'. Reorder the terms: -6q + 12q + q2 + -3q2 = -12q + 3q2 + 12q + -3q2 Combine like terms: -6q + 12q = 6q 6q + q2 + -3q2 = -12q + 3q2 + 12q + -3q2 Combine like terms: q2 + -3q2 = -2q2 6q + -2q2 = -12q + 3q2 + 12q + -3q2 Reorder the terms: 6q + -2q2 = -12q + 12q + 3q2 + -3q2 Combine like terms: -12q + 12q = 0 6q + -2q2 = 0 + 3q2 + -3q2 6q + -2q2 = 3q2 + -3q2 Combine like terms: 3q2 + -3q2 = 0 6q + -2q2 = 0 Factor out the Greatest Common Factor (GCF), '2q'. 2q(3 + -1q) = 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 = 3Solution
q = {0, 3}
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