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