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Simplifying 2a(2 + 3a) + -3a(2 + -6a) = 0 (2 * 2a + 3a * 2a) + -3a(2 + -6a) = 0 (4a + 6a2) + -3a(2 + -6a) = 0 4a + 6a2 + (2 * -3a + -6a * -3a) = 0 4a + 6a2 + (-6a + 18a2) = 0 Reorder the terms: 4a + -6a + 6a2 + 18a2 = 0 Combine like terms: 4a + -6a = -2a -2a + 6a2 + 18a2 = 0 Combine like terms: 6a2 + 18a2 = 24a2 -2a + 24a2 = 0 Solving -2a + 24a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(-1 + 12a) = 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 '(-1 + 12a)' equal to zero and attempt to solve: Simplifying -1 + 12a = 0 Solving -1 + 12a = 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 + 12a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 12a = 0 + 1 12a = 0 + 1 Combine like terms: 0 + 1 = 1 12a = 1 Divide each side by '12'. a = 0.08333333333 Simplifying a = 0.08333333333Solution
a = {0, 0.08333333333}
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