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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. (3a + 2c)(a + 3c) = 0Subproblem 1
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 = -0.6666666667cSubproblem 2
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 = -3cSolution
a = {-0.6666666667c, -3c}
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