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Simplifying 42q2 + -17qr + -15r2 = 0 Reorder the terms: -17qr + 42q2 + -15r2 = 0 Solving -17qr + 42q2 + -15r2 = 0 Solving for variable 'q'. Factor a trinomial. (6q + -5r)(7q + 3r) = 0Subproblem 1
Set the factor '(6q + -5r)' equal to zero and attempt to solve: Simplifying 6q + -5r = 0 Solving 6q + -5r = 0 Move all terms containing q to the left, all other terms to the right. Add '5r' to each side of the equation. 6q + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 6q + 0 = 0 + 5r 6q = 0 + 5r Remove the zero: 6q = 5r Divide each side by '6'. q = 0.8333333333r Simplifying q = 0.8333333333rSubproblem 2
Set the factor '(7q + 3r)' equal to zero and attempt to solve: Simplifying 7q + 3r = 0 Solving 7q + 3r = 0 Move all terms containing q to the left, all other terms to the right. Add '-3r' to each side of the equation. 7q + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 7q + 0 = 0 + -3r 7q = 0 + -3r Remove the zero: 7q = -3r Divide each side by '7'. q = -0.4285714286r Simplifying q = -0.4285714286rSolution
q = {0.8333333333r, -0.4285714286r}
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