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Simplifying 3q2 + -5q = 2q2 + -7q Reorder the terms: -5q + 3q2 = 2q2 + -7q Reorder the terms: -5q + 3q2 = -7q + 2q2 Solving -5q + 3q2 = -7q + 2q2 Solving for variable 'q'. Reorder the terms: -5q + 7q + 3q2 + -2q2 = -7q + 2q2 + 7q + -2q2 Combine like terms: -5q + 7q = 2q 2q + 3q2 + -2q2 = -7q + 2q2 + 7q + -2q2 Combine like terms: 3q2 + -2q2 = 1q2 2q + 1q2 = -7q + 2q2 + 7q + -2q2 Reorder the terms: 2q + 1q2 = -7q + 7q + 2q2 + -2q2 Combine like terms: -7q + 7q = 0 2q + 1q2 = 0 + 2q2 + -2q2 2q + 1q2 = 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 2q + 1q2 = 0 Factor out the Greatest Common Factor (GCF), 'q'. q(2 + q) = 0Subproblem 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 '(2 + q)' equal to zero and attempt to solve: Simplifying 2 + q = 0 Solving 2 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + q = 0 + -2 q = 0 + -2 Combine like terms: 0 + -2 = -2 q = -2 Simplifying q = -2Solution
q = {0, -2}
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