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Simplifying (2q + -1)(2q + 3) = 12 + -3q Reorder the terms: (-1 + 2q)(2q + 3) = 12 + -3q Reorder the terms: (-1 + 2q)(3 + 2q) = 12 + -3q Multiply (-1 + 2q) * (3 + 2q) (-1(3 + 2q) + 2q * (3 + 2q)) = 12 + -3q ((3 * -1 + 2q * -1) + 2q * (3 + 2q)) = 12 + -3q ((-3 + -2q) + 2q * (3 + 2q)) = 12 + -3q (-3 + -2q + (3 * 2q + 2q * 2q)) = 12 + -3q (-3 + -2q + (6q + 4q2)) = 12 + -3q Combine like terms: -2q + 6q = 4q (-3 + 4q + 4q2) = 12 + -3q Solving -3 + 4q + 4q2 = 12 + -3q Solving for variable 'q'. Reorder the terms: -3 + -12 + 4q + 3q + 4q2 = 12 + -3q + -12 + 3q Combine like terms: -3 + -12 = -15 -15 + 4q + 3q + 4q2 = 12 + -3q + -12 + 3q Combine like terms: 4q + 3q = 7q -15 + 7q + 4q2 = 12 + -3q + -12 + 3q Reorder the terms: -15 + 7q + 4q2 = 12 + -12 + -3q + 3q Combine like terms: 12 + -12 = 0 -15 + 7q + 4q2 = 0 + -3q + 3q -15 + 7q + 4q2 = -3q + 3q Combine like terms: -3q + 3q = 0 -15 + 7q + 4q2 = 0 Factor a trinomial. (-3 + -1q)(5 + -4q) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(5 + -4q)' equal to zero and attempt to solve: Simplifying 5 + -4q = 0 Solving 5 + -4q = 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 + -4q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4q = 0 + -5 -4q = 0 + -5 Combine like terms: 0 + -5 = -5 -4q = -5 Divide each side by '-4'. q = 1.25 Simplifying q = 1.25Solution
q = {-3, 1.25}
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