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Simplifying 3a2 + 21ab + 30b2 = 0 Reorder the terms: 21ab + 3a2 + 30b2 = 0 Solving 21ab + 3a2 + 30b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(7ab + a2 + 10b2) = 0 Factor a trinomial. 3((a + 2b)(a + 5b)) = 0 Ignore the factor 3.Subproblem 1
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 = -2bSubproblem 2
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 = -5bSolution
a = {-2b, -5b}
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