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Simplifying 2q(q + 1) + -1q(q + -1) = 0 Reorder the terms: 2q(1 + q) + -1q(q + -1) = 0 (1 * 2q + q * 2q) + -1q(q + -1) = 0 (2q + 2q2) + -1q(q + -1) = 0 Reorder the terms: 2q + 2q2 + -1q(-1 + q) = 0 2q + 2q2 + (-1 * -1q + q * -1q) = 0 2q + 2q2 + (1q + -1q2) = 0 Reorder the terms: 2q + 1q + 2q2 + -1q2 = 0 Combine like terms: 2q + 1q = 3q 3q + 2q2 + -1q2 = 0 Combine like terms: 2q2 + -1q2 = 1q2 3q + 1q2 = 0 Solving 3q + 1q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(3 + 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 '(3 + q)' equal to zero and attempt to solve: Simplifying 3 + q = 0 Solving 3 + q = 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 + q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + q = 0 + -3 q = 0 + -3 Combine like terms: 0 + -3 = -3 q = -3 Simplifying q = -3Solution
q = {0, -3}
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