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