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Simplifying 12a2 + -12ab + -9b2 = 0 Reorder the terms: -12ab + 12a2 + -9b2 = 0 Solving -12ab + 12a2 + -9b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4ab + 4a2 + -3b2) = 0 Factor a trinomial. 3((2a + -3b)(2a + b)) = 0 Ignore the factor 3.Subproblem 1
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 = 1.5bSubproblem 2
Set the factor '(2a + b)' equal to zero and attempt to solve: Simplifying 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5bSolution
a = {1.5b, -0.5b}
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