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Simplifying (5a + 3)(5 + -3a) = 0 Reorder the terms: (3 + 5a)(5 + -3a) = 0 Multiply (3 + 5a) * (5 + -3a) (3(5 + -3a) + 5a * (5 + -3a)) = 0 ((5 * 3 + -3a * 3) + 5a * (5 + -3a)) = 0 ((15 + -9a) + 5a * (5 + -3a)) = 0 (15 + -9a + (5 * 5a + -3a * 5a)) = 0 (15 + -9a + (25a + -15a2)) = 0 Combine like terms: -9a + 25a = 16a (15 + 16a + -15a2) = 0 Solving 15 + 16a + -15a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + -3a)(3 + 5a) = 0Subproblem 1
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 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 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve: Simplifying 3 + 5a = 0 Solving 3 + 5a = 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 + 5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5a = 0 + -3 5a = 0 + -3 Combine like terms: 0 + -3 = -3 5a = -3 Divide each side by '5'. a = -0.6 Simplifying a = -0.6Solution
a = {1.666666667, -0.6}
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