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Simplifying 3a2 + -11ac + 6c2 = 0 Reorder the terms: -11ac + 3a2 + 6c2 = 0 Solving -11ac + 3a2 + 6c2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -3c)(3a + -2c) = 0Subproblem 1
Set the factor '(a + -3c)' equal to zero and attempt to solve: Simplifying a + -3c = 0 Solving a + -3c = 0 Move all terms containing a to the left, all other terms to the right. Add '3c' to each side of the equation. a + -3c + 3c = 0 + 3c Combine like terms: -3c + 3c = 0 a + 0 = 0 + 3c a = 0 + 3c Remove the zero: a = 3c Simplifying a = 3cSubproblem 2
Set the factor '(3a + -2c)' equal to zero and attempt to solve: Simplifying 3a + -2c = 0 Solving 3a + -2c = 0 Move all terms containing a to the left, all other terms to the right. Add '2c' to each side of the equation. 3a + -2c + 2c = 0 + 2c Combine like terms: -2c + 2c = 0 3a + 0 = 0 + 2c 3a = 0 + 2c Remove the zero: 3a = 2c Divide each side by '3'. a = 0.6666666667c Simplifying a = 0.6666666667cSolution
a = {3c, 0.6666666667c}
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