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Simplifying 12a2 + -52ab + -40b2 = 0 Reorder the terms: -52ab + 12a2 + -40b2 = 0 Solving -52ab + 12a2 + -40b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-13ab + 3a2 + -10b2) = 0 Factor a trinomial. 4((a + -5b)(3a + 2b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(a + -5b)' equal to zero and attempt to solve: Simplifying a + -5b = 0 Solving a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 a + 0 = 0 + 5b a = 0 + 5b Remove the zero: a = 5b Simplifying a = 5bSubproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve: Simplifying 3a + 2b = 0 Solving 3a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 = 0 + -2b 3a = 0 + -2b Remove the zero: 3a = -2b Divide each side by '3'. a = -0.6666666667b Simplifying a = -0.6666666667bSolution
a = {5b, -0.6666666667b}
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