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Simplifying (q + 2)(3q + -4) = 0 Reorder the terms: (2 + q)(3q + -4) = 0 Reorder the terms: (2 + q)(-4 + 3q) = 0 Multiply (2 + q) * (-4 + 3q) (2(-4 + 3q) + q(-4 + 3q)) = 0 ((-4 * 2 + 3q * 2) + q(-4 + 3q)) = 0 ((-8 + 6q) + q(-4 + 3q)) = 0 (-8 + 6q + (-4 * q + 3q * q)) = 0 (-8 + 6q + (-4q + 3q2)) = 0 Combine like terms: 6q + -4q = 2q (-8 + 2q + 3q2) = 0 Solving -8 + 2q + 3q2 = 0 Solving for variable 'q'. Factor a trinomial. (-2 + -1q)(4 + -3q) = 0Subproblem 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 '(4 + -3q)' equal to zero and attempt to solve: Simplifying 4 + -3q = 0 Solving 4 + -3q = 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 + -3q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3q = 0 + -4 -3q = 0 + -4 Combine like terms: 0 + -4 = -4 -3q = -4 Divide each side by '-3'. q = 1.333333333 Simplifying q = 1.333333333Solution
q = {-2, 1.333333333}
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