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Simplifying 6a2 = 9 + 15a Solving 6a2 = 9 + 15a Solving for variable 'a'. Reorder the terms: -9 + -15a + 6a2 = 9 + 15a + -9 + -15a Reorder the terms: -9 + -15a + 6a2 = 9 + -9 + 15a + -15a Combine like terms: 9 + -9 = 0 -9 + -15a + 6a2 = 0 + 15a + -15a -9 + -15a + 6a2 = 15a + -15a Combine like terms: 15a + -15a = 0 -9 + -15a + 6a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -5a + 2a2) = 0 Factor a trinomial. 3((-1 + -2a)(3 + -1a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-0.5, 3}
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