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Simplifying (3a + 5)(a + 3) = 7 Reorder the terms: (5 + 3a)(a + 3) = 7 Reorder the terms: (5 + 3a)(3 + a) = 7 Multiply (5 + 3a) * (3 + a) (5(3 + a) + 3a * (3 + a)) = 7 ((3 * 5 + a * 5) + 3a * (3 + a)) = 7 ((15 + 5a) + 3a * (3 + a)) = 7 (15 + 5a + (3 * 3a + a * 3a)) = 7 (15 + 5a + (9a + 3a2)) = 7 Combine like terms: 5a + 9a = 14a (15 + 14a + 3a2) = 7 Solving 15 + 14a + 3a2 = 7 Solving for variable 'a'. Reorder the terms: 15 + -7 + 14a + 3a2 = 7 + -7 Combine like terms: 15 + -7 = 8 8 + 14a + 3a2 = 7 + -7 Combine like terms: 7 + -7 = 0 8 + 14a + 3a2 = 0 Factor a trinomial. (4 + a)(2 + 3a) = 0Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 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 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {-4, -0.6666666667}
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