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Simplifying (4a + 5)(7a + 2) = 0 Reorder the terms: (5 + 4a)(7a + 2) = 0 Reorder the terms: (5 + 4a)(2 + 7a) = 0 Multiply (5 + 4a) * (2 + 7a) (5(2 + 7a) + 4a * (2 + 7a)) = 0 ((2 * 5 + 7a * 5) + 4a * (2 + 7a)) = 0 ((10 + 35a) + 4a * (2 + 7a)) = 0 (10 + 35a + (2 * 4a + 7a * 4a)) = 0 (10 + 35a + (8a + 28a2)) = 0 Combine like terms: 35a + 8a = 43a (10 + 43a + 28a2) = 0 Solving 10 + 43a + 28a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + 4a)(2 + 7a) = 0Subproblem 1
Set the factor '(5 + 4a)' equal to zero and attempt to solve: Simplifying 5 + 4a = 0 Solving 5 + 4a = 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 + 4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4a = 0 + -5 4a = 0 + -5 Combine like terms: 0 + -5 = -5 4a = -5 Divide each side by '4'. a = -1.25 Simplifying a = -1.25Subproblem 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 = {-1.25, -0.2857142857}
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