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Simplifying 4a2 + -20ab + 24b2 = 0 Reorder the terms: -20ab + 4a2 + 24b2 = 0 Solving -20ab + 4a2 + 24b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5ab + a2 + 6b2) = 0 Factor a trinomial. 4((a + -3b)(a + -2b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(a + -3b)' equal to zero and attempt to solve: Simplifying a + -3b = 0 Solving a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 a + 0 = 0 + 3b a = 0 + 3b Remove the zero: a = 3b Simplifying a = 3bSubproblem 2
Set the factor '(a + -2b)' equal to zero and attempt to solve: Simplifying a + -2b = 0 Solving a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 a + 0 = 0 + 2b a = 0 + 2b Remove the zero: a = 2b Simplifying a = 2bSolution
a = {3b, 2b}
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