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Simplifying (4q + -5)(3q + 7) = 0 Reorder the terms: (-5 + 4q)(3q + 7) = 0 Reorder the terms: (-5 + 4q)(7 + 3q) = 0 Multiply (-5 + 4q) * (7 + 3q) (-5(7 + 3q) + 4q * (7 + 3q)) = 0 ((7 * -5 + 3q * -5) + 4q * (7 + 3q)) = 0 ((-35 + -15q) + 4q * (7 + 3q)) = 0 (-35 + -15q + (7 * 4q + 3q * 4q)) = 0 (-35 + -15q + (28q + 12q2)) = 0 Combine like terms: -15q + 28q = 13q (-35 + 13q + 12q2) = 0 Solving -35 + 13q + 12q2 = 0 Solving for variable 'q'. Factor a trinomial. (-7 + -3q)(5 + -4q) = 0Subproblem 1
Set the factor '(-7 + -3q)' equal to zero and attempt to solve: Simplifying -7 + -3q = 0 Solving -7 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3q = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3q = 0 + 7 -3q = 0 + 7 Combine like terms: 0 + 7 = 7 -3q = 7 Divide each side by '-3'. q = -2.333333333 Simplifying q = -2.333333333Subproblem 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 = {-2.333333333, 1.25}
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