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Simplifying (2a + 7)(a + 5) = 0 Reorder the terms: (7 + 2a)(a + 5) = 0 Reorder the terms: (7 + 2a)(5 + a) = 0 Multiply (7 + 2a) * (5 + a) (7(5 + a) + 2a * (5 + a)) = 0 ((5 * 7 + a * 7) + 2a * (5 + a)) = 0 ((35 + 7a) + 2a * (5 + a)) = 0 (35 + 7a + (5 * 2a + a * 2a)) = 0 (35 + 7a + (10a + 2a2)) = 0 Combine like terms: 7a + 10a = 17a (35 + 17a + 2a2) = 0 Solving 35 + 17a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + a)(7 + 2a) = 0Subproblem 1
Set the factor '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Subproblem 2
Set the factor '(7 + 2a)' equal to zero and attempt to solve: Simplifying 7 + 2a = 0 Solving 7 + 2a = 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 + 2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2a = 0 + -7 2a = 0 + -7 Combine like terms: 0 + -7 = -7 2a = -7 Divide each side by '2'. a = -3.5 Simplifying a = -3.5Solution
a = {-5, -3.5}
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