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Simplifying 3a(4 + -1a) + -4a(a + 6) = 0 (4 * 3a + -1a * 3a) + -4a(a + 6) = 0 (12a + -3a2) + -4a(a + 6) = 0 Reorder the terms: 12a + -3a2 + -4a(6 + a) = 0 12a + -3a2 + (6 * -4a + a * -4a) = 0 12a + -3a2 + (-24a + -4a2) = 0 Reorder the terms: 12a + -24a + -3a2 + -4a2 = 0 Combine like terms: 12a + -24a = -12a -12a + -3a2 + -4a2 = 0 Combine like terms: -3a2 + -4a2 = -7a2 -12a + -7a2 = 0 Solving -12a + -7a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1a'. -1a(12 + 7a) = 0 Ignore the factor -1.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 '(12 + 7a)' equal to zero and attempt to solve: Simplifying 12 + 7a = 0 Solving 12 + 7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 7a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 7a = 0 + -12 7a = 0 + -12 Combine like terms: 0 + -12 = -12 7a = -12 Divide each side by '7'. a = -1.714285714 Simplifying a = -1.714285714Solution
a = {0, -1.714285714}
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