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Simplifying q(q + 8) + q(q + -3) = 0 Reorder the terms: q(8 + q) + q(q + -3) = 0 (8 * q + q * q) + q(q + -3) = 0 (8q + q2) + q(q + -3) = 0 Reorder the terms: 8q + q2 + q(-3 + q) = 0 8q + q2 + (-3 * q + q * q) = 0 8q + q2 + (-3q + q2) = 0 Reorder the terms: 8q + -3q + q2 + q2 = 0 Combine like terms: 8q + -3q = 5q 5q + q2 + q2 = 0 Combine like terms: q2 + q2 = 2q2 5q + 2q2 = 0 Solving 5q + 2q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(5 + 2q) = 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 '(5 + 2q)' equal to zero and attempt to solve: Simplifying 5 + 2q = 0 Solving 5 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2q = 0 + -5 2q = 0 + -5 Combine like terms: 0 + -5 = -5 2q = -5 Divide each side by '2'. q = -2.5 Simplifying q = -2.5Solution
q = {0, -2.5}
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