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Simplifying (3q + 6)(8q + -2) = 0 Reorder the terms: (6 + 3q)(8q + -2) = 0 Reorder the terms: (6 + 3q)(-2 + 8q) = 0 Multiply (6 + 3q) * (-2 + 8q) (6(-2 + 8q) + 3q * (-2 + 8q)) = 0 ((-2 * 6 + 8q * 6) + 3q * (-2 + 8q)) = 0 ((-12 + 48q) + 3q * (-2 + 8q)) = 0 (-12 + 48q + (-2 * 3q + 8q * 3q)) = 0 (-12 + 48q + (-6q + 24q2)) = 0 Combine like terms: 48q + -6q = 42q (-12 + 42q + 24q2) = 0 Solving -12 + 42q + 24q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + 7q + 4q2) = 0 Factor a trinomial. 6((-2 + -1q)(1 + -4q)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -1q)' equal to zero and attempt to solve: Simplifying -2 + -1q = 0 Solving -2 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1q = 0 + 2 -1q = 0 + 2 Combine like terms: 0 + 2 = 2 -1q = 2 Divide each side by '-1'. q = -2 Simplifying q = -2Subproblem 2
Set the factor '(1 + -4q)' equal to zero and attempt to solve: Simplifying 1 + -4q = 0 Solving 1 + -4q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4q = 0 + -1 -4q = 0 + -1 Combine like terms: 0 + -1 = -1 -4q = -1 Divide each side by '-4'. q = 0.25 Simplifying q = 0.25Solution
q = {-2, 0.25}
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