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Simplifying 12a2 + 16ab + -3b2 = 0 Reorder the terms: 16ab + 12a2 + -3b2 = 0 Solving 16ab + 12a2 + -3b2 = 0 Solving for variable 'a'. Factor a trinomial. (6a + -1b)(2a + 3b) = 0Subproblem 1
Set the factor '(6a + -1b)' equal to zero and attempt to solve: Simplifying 6a + -1b = 0 Solving 6a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 6a + -1b + b = 0 + b Combine like terms: -1b + b = 0 6a + 0 = 0 + b 6a = 0 + b Remove the zero: 6a = b Divide each side by '6'. a = 0.1666666667b Simplifying a = 0.1666666667bSubproblem 2
Set the factor '(2a + 3b)' equal to zero and attempt to solve: Simplifying 2a + 3b = 0 Solving 2a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 2a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 2a + 0 = 0 + -3b 2a = 0 + -3b Remove the zero: 2a = -3b Divide each side by '2'. a = -1.5b Simplifying a = -1.5bSolution
a = {0.1666666667b, -1.5b}
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