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Simplifying 12a2 + 11ar + -15r2 = 0 Reorder the terms: 11ar + 12a2 + -15r2 = 0 Solving 11ar + 12a2 + -15r2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -3r)(3a + 5r) = 0Subproblem 1
Set the factor '(4a + -3r)' equal to zero and attempt to solve: Simplifying 4a + -3r = 0 Solving 4a + -3r = 0 Move all terms containing a to the left, all other terms to the right. Add '3r' to each side of the equation. 4a + -3r + 3r = 0 + 3r Combine like terms: -3r + 3r = 0 4a + 0 = 0 + 3r 4a = 0 + 3r Remove the zero: 4a = 3r Divide each side by '4'. a = 0.75r Simplifying a = 0.75rSubproblem 2
Set the factor '(3a + 5r)' equal to zero and attempt to solve: Simplifying 3a + 5r = 0 Solving 3a + 5r = 0 Move all terms containing a to the left, all other terms to the right. Add '-5r' to each side of the equation. 3a + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 3a + 0 = 0 + -5r 3a = 0 + -5r Remove the zero: 3a = -5r Divide each side by '3'. a = -1.666666667r Simplifying a = -1.666666667rSolution
a = {0.75r, -1.666666667r}
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