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Simplifying 5q(6 + -4q) + 8q2 = 0 (6 * 5q + -4q * 5q) + 8q2 = 0 (30q + -20q2) + 8q2 = 0 Combine like terms: -20q2 + 8q2 = -12q2 30q + -12q2 = 0 Solving 30q + -12q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '6q'. 6q(5 + -2q) = 0 Ignore the factor 6.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 '(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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