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Simplifying 3q2 + -24q + 72 = q2 + -12q + 72 Reorder the terms: 72 + -24q + 3q2 = q2 + -12q + 72 Reorder the terms: 72 + -24q + 3q2 = 72 + -12q + q2 Add '-72' to each side of the equation. 72 + -24q + -72 + 3q2 = 72 + -12q + -72 + q2 Reorder the terms: 72 + -72 + -24q + 3q2 = 72 + -12q + -72 + q2 Combine like terms: 72 + -72 = 0 0 + -24q + 3q2 = 72 + -12q + -72 + q2 -24q + 3q2 = 72 + -12q + -72 + q2 Reorder the terms: -24q + 3q2 = 72 + -72 + -12q + q2 Combine like terms: 72 + -72 = 0 -24q + 3q2 = 0 + -12q + q2 -24q + 3q2 = -12q + q2 Solving -24q + 3q2 = -12q + q2 Solving for variable 'q'. Reorder the terms: -24q + 12q + 3q2 + -1q2 = -12q + q2 + 12q + -1q2 Combine like terms: -24q + 12q = -12q -12q + 3q2 + -1q2 = -12q + q2 + 12q + -1q2 Combine like terms: 3q2 + -1q2 = 2q2 -12q + 2q2 = -12q + q2 + 12q + -1q2 Reorder the terms: -12q + 2q2 = -12q + 12q + q2 + -1q2 Combine like terms: -12q + 12q = 0 -12q + 2q2 = 0 + q2 + -1q2 -12q + 2q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 -12q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2q'. 2q(-6 + q) = 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 '(-6 + q)' equal to zero and attempt to solve: Simplifying -6 + q = 0 Solving -6 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = 0 + 6 Combine like terms: -6 + 6 = 0 0 + q = 0 + 6 q = 0 + 6 Combine like terms: 0 + 6 = 6 q = 6 Simplifying q = 6Solution
q = {0, 6}
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