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Simplifying (4a + 3)(8a + 7) = 0 Reorder the terms: (3 + 4a)(8a + 7) = 0 Reorder the terms: (3 + 4a)(7 + 8a) = 0 Multiply (3 + 4a) * (7 + 8a) (3(7 + 8a) + 4a * (7 + 8a)) = 0 ((7 * 3 + 8a * 3) + 4a * (7 + 8a)) = 0 ((21 + 24a) + 4a * (7 + 8a)) = 0 (21 + 24a + (7 * 4a + 8a * 4a)) = 0 (21 + 24a + (28a + 32a2)) = 0 Combine like terms: 24a + 28a = 52a (21 + 52a + 32a2) = 0 Solving 21 + 52a + 32a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + 8a)(3 + 4a) = 0Subproblem 1
Set the factor '(7 + 8a)' equal to zero and attempt to solve: Simplifying 7 + 8a = 0 Solving 7 + 8a = 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 + 8a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8a = 0 + -7 8a = 0 + -7 Combine like terms: 0 + -7 = -7 8a = -7 Divide each side by '8'. a = -0.875 Simplifying a = -0.875Subproblem 2
Set the factor '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 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 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75Solution
a = {-0.875, -0.75}
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