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Simplifying (a + 4)(7a + 8) = 0 Reorder the terms: (4 + a)(7a + 8) = 0 Reorder the terms: (4 + a)(8 + 7a) = 0 Multiply (4 + a) * (8 + 7a) (4(8 + 7a) + a(8 + 7a)) = 0 ((8 * 4 + 7a * 4) + a(8 + 7a)) = 0 ((32 + 28a) + a(8 + 7a)) = 0 (32 + 28a + (8 * a + 7a * a)) = 0 (32 + 28a + (8a + 7a2)) = 0 Combine like terms: 28a + 8a = 36a (32 + 36a + 7a2) = 0 Solving 32 + 36a + 7a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + a)(8 + 7a) = 0Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 2
Set the factor '(8 + 7a)' equal to zero and attempt to solve: Simplifying 8 + 7a = 0 Solving 8 + 7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7a = 0 + -8 7a = 0 + -8 Combine like terms: 0 + -8 = -8 7a = -8 Divide each side by '7'. a = -1.142857143 Simplifying a = -1.142857143Solution
a = {-4, -1.142857143}
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