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Simplifying (2a + 12)(14a + 4) = 0 Reorder the terms: (12 + 2a)(14a + 4) = 0 Reorder the terms: (12 + 2a)(4 + 14a) = 0 Multiply (12 + 2a) * (4 + 14a) (12(4 + 14a) + 2a * (4 + 14a)) = 0 ((4 * 12 + 14a * 12) + 2a * (4 + 14a)) = 0 ((48 + 168a) + 2a * (4 + 14a)) = 0 (48 + 168a + (4 * 2a + 14a * 2a)) = 0 (48 + 168a + (8a + 28a2)) = 0 Combine like terms: 168a + 8a = 176a (48 + 176a + 28a2) = 0 Solving 48 + 176a + 28a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 44a + 7a2) = 0 Factor a trinomial. 4((6 + a)(2 + 7a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve: Simplifying 6 + a = 0 Solving 6 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + a = 0 + -6 a = 0 + -6 Combine like terms: 0 + -6 = -6 a = -6 Simplifying a = -6Subproblem 2
Set the factor '(2 + 7a)' equal to zero and attempt to solve: Simplifying 2 + 7a = 0 Solving 2 + 7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7a = 0 + -2 7a = 0 + -2 Combine like terms: 0 + -2 = -2 7a = -2 Divide each side by '7'. a = -0.2857142857 Simplifying a = -0.2857142857Solution
a = {-6, -0.2857142857}
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