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Simplifying 2a(a + -5) + -3a(4a + 6) = 0 Reorder the terms: 2a(-5 + a) + -3a(4a + 6) = 0 (-5 * 2a + a * 2a) + -3a(4a + 6) = 0 (-10a + 2a2) + -3a(4a + 6) = 0 Reorder the terms: -10a + 2a2 + -3a(6 + 4a) = 0 -10a + 2a2 + (6 * -3a + 4a * -3a) = 0 -10a + 2a2 + (-18a + -12a2) = 0 Reorder the terms: -10a + -18a + 2a2 + -12a2 = 0 Combine like terms: -10a + -18a = -28a -28a + 2a2 + -12a2 = 0 Combine like terms: 2a2 + -12a2 = -10a2 -28a + -10a2 = 0 Solving -28a + -10a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-2a'. -2a(14 + 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 '(14 + 5a)' equal to zero and attempt to solve: Simplifying 14 + 5a = 0 Solving 14 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 5a = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 5a = 0 + -14 5a = 0 + -14 Combine like terms: 0 + -14 = -14 5a = -14 Divide each side by '5'. a = -2.8 Simplifying a = -2.8Solution
a = {0, -2.8}
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