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Simplifying (7a + 4)(8a + 3) = 0 Reorder the terms: (4 + 7a)(8a + 3) = 0 Reorder the terms: (4 + 7a)(3 + 8a) = 0 Multiply (4 + 7a) * (3 + 8a) (4(3 + 8a) + 7a * (3 + 8a)) = 0 ((3 * 4 + 8a * 4) + 7a * (3 + 8a)) = 0 ((12 + 32a) + 7a * (3 + 8a)) = 0 (12 + 32a + (3 * 7a + 8a * 7a)) = 0 (12 + 32a + (21a + 56a2)) = 0 Combine like terms: 32a + 21a = 53a (12 + 53a + 56a2) = 0 Solving 12 + 53a + 56a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + 7a)(3 + 8a) = 0Subproblem 1
Set the factor '(4 + 7a)' equal to zero and attempt to solve: Simplifying 4 + 7a = 0 Solving 4 + 7a = 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 + 7a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7a = 0 + -4 7a = 0 + -4 Combine like terms: 0 + -4 = -4 7a = -4 Divide each side by '7'. a = -0.5714285714 Simplifying a = -0.5714285714Subproblem 2
Set the factor '(3 + 8a)' equal to zero and attempt to solve: Simplifying 3 + 8a = 0 Solving 3 + 8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 8a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8a = 0 + -3 8a = 0 + -3 Combine like terms: 0 + -3 = -3 8a = -3 Divide each side by '8'. a = -0.375 Simplifying a = -0.375Solution
a = {-0.5714285714, -0.375}
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