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Simplifying 6(2a2 + 3a) = 18 + -12a Reorder the terms: 6(3a + 2a2) = 18 + -12a (3a * 6 + 2a2 * 6) = 18 + -12a (18a + 12a2) = 18 + -12a Solving 18a + 12a2 = 18 + -12a Solving for variable 'a'. Reorder the terms: -18 + 18a + 12a + 12a2 = 18 + -12a + -18 + 12a Combine like terms: 18a + 12a = 30a -18 + 30a + 12a2 = 18 + -12a + -18 + 12a Reorder the terms: -18 + 30a + 12a2 = 18 + -18 + -12a + 12a Combine like terms: 18 + -18 = 0 -18 + 30a + 12a2 = 0 + -12a + 12a -18 + 30a + 12a2 = -12a + 12a Combine like terms: -12a + 12a = 0 -18 + 30a + 12a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 5a + 2a2) = 0 Factor a trinomial. 6((-3 + -1a)(1 + -2a)) = 0 Ignore the factor 6.Subproblem 1
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 = -3Subproblem 2
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 = 0.5Solution
a = {-3, 0.5}
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