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Simplifying (q + -9)(5q + -12) = 0 Reorder the terms: (-9 + q)(5q + -12) = 0 Reorder the terms: (-9 + q)(-12 + 5q) = 0 Multiply (-9 + q) * (-12 + 5q) (-9(-12 + 5q) + q(-12 + 5q)) = 0 ((-12 * -9 + 5q * -9) + q(-12 + 5q)) = 0 ((108 + -45q) + q(-12 + 5q)) = 0 (108 + -45q + (-12 * q + 5q * q)) = 0 (108 + -45q + (-12q + 5q2)) = 0 Combine like terms: -45q + -12q = -57q (108 + -57q + 5q2) = 0 Solving 108 + -57q + 5q2 = 0 Solving for variable 'q'. Factor a trinomial. (12 + -5q)(9 + -1q) = 0Subproblem 1
Set the factor '(12 + -5q)' equal to zero and attempt to solve: Simplifying 12 + -5q = 0 Solving 12 + -5q = 0 Move all terms containing q to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5q = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5q = 0 + -12 -5q = 0 + -12 Combine like terms: 0 + -12 = -12 -5q = -12 Divide each side by '-5'. q = 2.4 Simplifying q = 2.4Subproblem 2
Set the factor '(9 + -1q)' equal to zero and attempt to solve: Simplifying 9 + -1q = 0 Solving 9 + -1q = 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 + -1q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1q = 0 + -9 -1q = 0 + -9 Combine like terms: 0 + -9 = -9 -1q = -9 Divide each side by '-1'. q = 9 Simplifying q = 9Solution
q = {2.4, 9}
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