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Simplifying 6a2 + 13ar + 6r2 = 0 Reorder the terms: 13ar + 6a2 + 6r2 = 0 Solving 13ar + 6a2 + 6r2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + 2r)(2a + 3r) = 0Subproblem 1
Set the factor '(3a + 2r)' equal to zero and attempt to solve: Simplifying 3a + 2r = 0 Solving 3a + 2r = 0 Move all terms containing a to the left, all other terms to the right. Add '-2r' to each side of the equation. 3a + 2r + -2r = 0 + -2r Combine like terms: 2r + -2r = 0 3a + 0 = 0 + -2r 3a = 0 + -2r Remove the zero: 3a = -2r Divide each side by '3'. a = -0.6666666667r Simplifying a = -0.6666666667rSubproblem 2
Set the factor '(2a + 3r)' equal to zero and attempt to solve: Simplifying 2a + 3r = 0 Solving 2a + 3r = 0 Move all terms containing a to the left, all other terms to the right. Add '-3r' to each side of the equation. 2a + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 2a + 0 = 0 + -3r 2a = 0 + -3r Remove the zero: 2a = -3r Divide each side by '2'. a = -1.5r Simplifying a = -1.5rSolution
a = {-0.6666666667r, -1.5r}
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