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Simplifying 27a2 + -12ab + -32b2 = 0 Reorder the terms: -12ab + 27a2 + -32b2 = 0 Solving -12ab + 27a2 + -32b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -4b)(9a + 8b) = 0Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve: Simplifying 3a + -4b = 0 Solving 3a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 3a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 3a + 0 = 0 + 4b 3a = 0 + 4b Remove the zero: 3a = 4b Divide each side by '3'. a = 1.333333333b Simplifying a = 1.333333333bSubproblem 2
Set the factor '(9a + 8b)' equal to zero and attempt to solve: Simplifying 9a + 8b = 0 Solving 9a + 8b = 0 Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 9a + 8b + -8b = 0 + -8b Combine like terms: 8b + -8b = 0 9a + 0 = 0 + -8b 9a = 0 + -8b Remove the zero: 9a = -8b Divide each side by '9'. a = -0.8888888889b Simplifying a = -0.8888888889bSolution
a = {1.333333333b, -0.8888888889b}
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