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Simplifying 5a(a + -2) + 3a(2a + 5) = 0 Reorder the terms: 5a(-2 + a) + 3a(2a + 5) = 0 (-2 * 5a + a * 5a) + 3a(2a + 5) = 0 (-10a + 5a2) + 3a(2a + 5) = 0 Reorder the terms: -10a + 5a2 + 3a(5 + 2a) = 0 -10a + 5a2 + (5 * 3a + 2a * 3a) = 0 -10a + 5a2 + (15a + 6a2) = 0 Reorder the terms: -10a + 15a + 5a2 + 6a2 = 0 Combine like terms: -10a + 15a = 5a 5a + 5a2 + 6a2 = 0 Combine like terms: 5a2 + 6a2 = 11a2 5a + 11a2 = 0 Solving 5a + 11a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(5 + 11a) = 0Subproblem 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 '(5 + 11a)' equal to zero and attempt to solve: Simplifying 5 + 11a = 0 Solving 5 + 11a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 11a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 11a = 0 + -5 11a = 0 + -5 Combine like terms: 0 + -5 = -5 11a = -5 Divide each side by '11'. a = -0.4545454545 Simplifying a = -0.4545454545Solution
a = {0, -0.4545454545}
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