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Simplifying (6q + 10)(q + -3) = 0 Reorder the terms: (10 + 6q)(q + -3) = 0 Reorder the terms: (10 + 6q)(-3 + q) = 0 Multiply (10 + 6q) * (-3 + q) (10(-3 + q) + 6q * (-3 + q)) = 0 ((-3 * 10 + q * 10) + 6q * (-3 + q)) = 0 ((-30 + 10q) + 6q * (-3 + q)) = 0 (-30 + 10q + (-3 * 6q + q * 6q)) = 0 (-30 + 10q + (-18q + 6q2)) = 0 Combine like terms: 10q + -18q = -8q (-30 + -8q + 6q2) = 0 Solving -30 + -8q + 6q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -4q + 3q2) = 0 Factor a trinomial. 2((-5 + -3q)(3 + -1q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -3q)' equal to zero and attempt to solve: Simplifying -5 + -3q = 0 Solving -5 + -3q = 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 + -3q = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3q = 0 + 5 -3q = 0 + 5 Combine like terms: 0 + 5 = 5 -3q = 5 Divide each side by '-3'. q = -1.666666667 Simplifying q = -1.666666667Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve: Simplifying 3 + -1q = 0 Solving 3 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1q = 0 + -3 -1q = 0 + -3 Combine like terms: 0 + -3 = -3 -1q = -3 Divide each side by '-1'. q = 3 Simplifying q = 3Solution
q = {-1.666666667, 3}
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