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Simplifying 20a3 = -18a2 + 18a Reorder the terms: 20a3 = 18a + -18a2 Solving 20a3 = 18a + -18a2 Solving for variable 'a'. Reorder the terms: -18a + 18a2 + 20a3 = 18a + -18a2 + -18a + 18a2 Reorder the terms: -18a + 18a2 + 20a3 = 18a + -18a + -18a2 + 18a2 Combine like terms: 18a + -18a = 0 -18a + 18a2 + 20a3 = 0 + -18a2 + 18a2 -18a + 18a2 + 20a3 = -18a2 + 18a2 Combine like terms: -18a2 + 18a2 = 0 -18a + 18a2 + 20a3 = 0 Factor out the Greatest Common Factor (GCF), '2a'. 2a(-9 + 9a + 10a2) = 0 Factor a trinomial. 2a((-3 + -2a)(3 + -5a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5Subproblem 3
Set the factor '(3 + -5a)' equal to zero and attempt to solve: Simplifying 3 + -5a = 0 Solving 3 + -5a = 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 + -5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5a = 0 + -3 -5a = 0 + -3 Combine like terms: 0 + -3 = -3 -5a = -3 Divide each side by '-5'. a = 0.6 Simplifying a = 0.6Solution
a = {0, -1.5, 0.6}
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