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Simplifying (5a + 8)(a + 7) = 0 Reorder the terms: (8 + 5a)(a + 7) = 0 Reorder the terms: (8 + 5a)(7 + a) = 0 Multiply (8 + 5a) * (7 + a) (8(7 + a) + 5a * (7 + a)) = 0 ((7 * 8 + a * 8) + 5a * (7 + a)) = 0 ((56 + 8a) + 5a * (7 + a)) = 0 (56 + 8a + (7 * 5a + a * 5a)) = 0 (56 + 8a + (35a + 5a2)) = 0 Combine like terms: 8a + 35a = 43a (56 + 43a + 5a2) = 0 Solving 56 + 43a + 5a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + a)(8 + 5a) = 0Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Subproblem 2
Set the factor '(8 + 5a)' equal to zero and attempt to solve: Simplifying 8 + 5a = 0 Solving 8 + 5a = 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 + 5a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5a = 0 + -8 5a = 0 + -8 Combine like terms: 0 + -8 = -8 5a = -8 Divide each side by '5'. a = -1.6 Simplifying a = -1.6Solution
a = {-7, -1.6}
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