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Simplifying 6a(4a + -2) + 3a(a + 7) = 0 Reorder the terms: 6a(-2 + 4a) + 3a(a + 7) = 0 (-2 * 6a + 4a * 6a) + 3a(a + 7) = 0 (-12a + 24a2) + 3a(a + 7) = 0 Reorder the terms: -12a + 24a2 + 3a(7 + a) = 0 -12a + 24a2 + (7 * 3a + a * 3a) = 0 -12a + 24a2 + (21a + 3a2) = 0 Reorder the terms: -12a + 21a + 24a2 + 3a2 = 0 Combine like terms: -12a + 21a = 9a 9a + 24a2 + 3a2 = 0 Combine like terms: 24a2 + 3a2 = 27a2 9a + 27a2 = 0 Solving 9a + 27a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '9a'. 9a(1 + 3a) = 0 Ignore the factor 9.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 + 3a)' equal to zero and attempt to solve: Simplifying 1 + 3a = 0 Solving 1 + 3a = 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 + 3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3a = 0 + -1 3a = 0 + -1 Combine like terms: 0 + -1 = -1 3a = -1 Divide each side by '3'. a = -0.3333333333 Simplifying a = -0.3333333333Solution
a = {0, -0.3333333333}
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