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Simplifying 5a2 + 10ab + -15b2 = 0 Reorder the terms: 10ab + 5a2 + -15b2 = 0 Solving 10ab + 5a2 + -15b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(2ab + a2 + -3b2) = 0 Factor a trinomial. 5((a + -1b)(a + 3b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(a + -1b)' equal to zero and attempt to solve: Simplifying a + -1b = 0 Solving a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. a + -1b + b = 0 + b Combine like terms: -1b + b = 0 a + 0 = 0 + b a = 0 + b Remove the zero: a = b Simplifying a = bSubproblem 2
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 = -3bSolution
a = {b, -3b}
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