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Simplifying (q + 14)(3q + -15) = 0 Reorder the terms: (14 + q)(3q + -15) = 0 Reorder the terms: (14 + q)(-15 + 3q) = 0 Multiply (14 + q) * (-15 + 3q) (14(-15 + 3q) + q(-15 + 3q)) = 0 ((-15 * 14 + 3q * 14) + q(-15 + 3q)) = 0 ((-210 + 42q) + q(-15 + 3q)) = 0 (-210 + 42q + (-15 * q + 3q * q)) = 0 (-210 + 42q + (-15q + 3q2)) = 0 Combine like terms: 42q + -15q = 27q (-210 + 27q + 3q2) = 0 Solving -210 + 27q + 3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(-70 + 9q + q2) = 0 Factor a trinomial. 3((-14 + -1q)(5 + -1q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-14 + -1q)' equal to zero and attempt to solve: Simplifying -14 + -1q = 0 Solving -14 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1q = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1q = 0 + 14 -1q = 0 + 14 Combine like terms: 0 + 14 = 14 -1q = 14 Divide each side by '-1'. q = -14 Simplifying q = -14Subproblem 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 = {-14, 5}
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