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Simplifying (q + 4)(3q + -15) = 0 Reorder the terms: (4 + q)(3q + -15) = 0 Reorder the terms: (4 + q)(-15 + 3q) = 0 Multiply (4 + q) * (-15 + 3q) (4(-15 + 3q) + q(-15 + 3q)) = 0 ((-15 * 4 + 3q * 4) + q(-15 + 3q)) = 0 ((-60 + 12q) + q(-15 + 3q)) = 0 (-60 + 12q + (-15 * q + 3q * q)) = 0 (-60 + 12q + (-15q + 3q2)) = 0 Combine like terms: 12q + -15q = -3q (-60 + -3q + 3q2) = 0 Solving -60 + -3q + 3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + -1q + q2) = 0 Factor a trinomial. 3((-4 + -1q)(5 + -1q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -1q)' equal to zero and attempt to solve: Simplifying -4 + -1q = 0 Solving -4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1q = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1q = 0 + 4 -1q = 0 + 4 Combine like terms: 0 + 4 = 4 -1q = 4 Divide each side by '-1'. q = -4 Simplifying q = -4Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve: Simplifying 5 + -1q = 0 Solving 5 + -1q = 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 + -1q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1q = 0 + -5 -1q = 0 + -5 Combine like terms: 0 + -5 = -5 -1q = -5 Divide each side by '-1'. q = 5 Simplifying q = 5Solution
q = {-4, 5}
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