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Simplifying (4q + 5)(3q + -5) = 0 Reorder the terms: (5 + 4q)(3q + -5) = 0 Reorder the terms: (5 + 4q)(-5 + 3q) = 0 Multiply (5 + 4q) * (-5 + 3q) (5(-5 + 3q) + 4q * (-5 + 3q)) = 0 ((-5 * 5 + 3q * 5) + 4q * (-5 + 3q)) = 0 ((-25 + 15q) + 4q * (-5 + 3q)) = 0 (-25 + 15q + (-5 * 4q + 3q * 4q)) = 0 (-25 + 15q + (-20q + 12q2)) = 0 Combine like terms: 15q + -20q = -5q (-25 + -5q + 12q2) = 0 Solving -25 + -5q + 12q2 = 0 Solving for variable 'q'. Factor a trinomial. (-5 + -4q)(5 + -3q) = 0Subproblem 1
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 = -1.25Subproblem 2
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 = 1.666666667Solution
q = {-1.25, 1.666666667}
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