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Simplifying 6a2b2 + 11abc + 4c2 = 0 Reorder the terms: 11abc + 6a2b2 + 4c2 = 0 Solving 11abc + 6a2b2 + 4c2 = 0 Solving for variable 'a'. Factor a trinomial. (2ab + c)(3ab + 4c) = 0Subproblem 1
Set the factor '(2ab + c)' equal to zero and attempt to solve: Simplifying 2ab + c = 0 Solving 2ab + c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. 2ab + c + -1c = 0 + -1c Combine like terms: c + -1c = 0 2ab + 0 = 0 + -1c 2ab = 0 + -1c Remove the zero: 2ab = -1c Divide each side by '2b'. a = -0.5b-1c Simplifying a = -0.5b-1cSubproblem 2
Set the factor '(3ab + 4c)' equal to zero and attempt to solve: Simplifying 3ab + 4c = 0 Solving 3ab + 4c = 0 Move all terms containing a to the left, all other terms to the right. Add '-4c' to each side of the equation. 3ab + 4c + -4c = 0 + -4c Combine like terms: 4c + -4c = 0 3ab + 0 = 0 + -4c 3ab = 0 + -4c Remove the zero: 3ab = -4c Divide each side by '3b'. a = -1.333333333b-1c Simplifying a = -1.333333333b-1cSolution
a = {-0.5b-1c, -1.333333333b-1c}
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