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Simplifying 30a2 + -186a + -432 = 0 Reorder the terms: -432 + -186a + 30a2 = 0 Solving -432 + -186a + 30a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(-72 + -31a + 5a2) = 0 Factor a trinomial. 6((-9 + -5a)(8 + -1a)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -5a)' equal to zero and attempt to solve: Simplifying -9 + -5a = 0 Solving -9 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5a = 0 + 9 -5a = 0 + 9 Combine like terms: 0 + 9 = 9 -5a = 9 Divide each side by '-5'. a = -1.8 Simplifying a = -1.8Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8Solution
a = {-1.8, 8}
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