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Simplifying 12q2 + -11qr + -15r2 = 0 Reorder the terms: -11qr + 12q2 + -15r2 = 0 Solving -11qr + 12q2 + -15r2 = 0 Solving for variable 'q'. Factor a trinomial. (3q + -5r)(4q + 3r) = 0Subproblem 1
Set the factor '(3q + -5r)' equal to zero and attempt to solve: Simplifying 3q + -5r = 0 Solving 3q + -5r = 0 Move all terms containing q to the left, all other terms to the right. Add '5r' to each side of the equation. 3q + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 3q + 0 = 0 + 5r 3q = 0 + 5r Remove the zero: 3q = 5r Divide each side by '3'. q = 1.666666667r Simplifying q = 1.666666667rSubproblem 2
Set the factor '(4q + 3r)' equal to zero and attempt to solve: Simplifying 4q + 3r = 0 Solving 4q + 3r = 0 Move all terms containing q to the left, all other terms to the right. Add '-3r' to each side of the equation. 4q + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 4q + 0 = 0 + -3r 4q = 0 + -3r Remove the zero: 4q = -3r Divide each side by '4'. q = -0.75r Simplifying q = -0.75rSolution
q = {1.666666667r, -0.75r}
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