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Simplifying q(2 + 3q) + -1q(5q + -7) = 0 (2 * q + 3q * q) + -1q(5q + -7) = 0 (2q + 3q2) + -1q(5q + -7) = 0 Reorder the terms: 2q + 3q2 + -1q(-7 + 5q) = 0 2q + 3q2 + (-7 * -1q + 5q * -1q) = 0 2q + 3q2 + (7q + -5q2) = 0 Reorder the terms: 2q + 7q + 3q2 + -5q2 = 0 Combine like terms: 2q + 7q = 9q 9q + 3q2 + -5q2 = 0 Combine like terms: 3q2 + -5q2 = -2q2 9q + -2q2 = 0 Solving 9q + -2q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(9 + -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 '(9 + -2q)' equal to zero and attempt to solve: Simplifying 9 + -2q = 0 Solving 9 + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2q = 0 + -9 -2q = 0 + -9 Combine like terms: 0 + -9 = -9 -2q = -9 Divide each side by '-2'. q = 4.5 Simplifying q = 4.5Solution
q = {0, 4.5}
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