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Simplifying (2a + 3)(a + -5) + (4a + -5)(a + -5) = 0 Reorder the terms: (3 + 2a)(a + -5) + (4a + -5)(a + -5) = 0 Reorder the terms: (3 + 2a)(-5 + a) + (4a + -5)(a + -5) = 0 Multiply (3 + 2a) * (-5 + a) (3(-5 + a) + 2a * (-5 + a)) + (4a + -5)(a + -5) = 0 ((-5 * 3 + a * 3) + 2a * (-5 + a)) + (4a + -5)(a + -5) = 0 ((-15 + 3a) + 2a * (-5 + a)) + (4a + -5)(a + -5) = 0 (-15 + 3a + (-5 * 2a + a * 2a)) + (4a + -5)(a + -5) = 0 (-15 + 3a + (-10a + 2a2)) + (4a + -5)(a + -5) = 0 Combine like terms: 3a + -10a = -7a (-15 + -7a + 2a2) + (4a + -5)(a + -5) = 0 Reorder the terms: -15 + -7a + 2a2 + (-5 + 4a)(a + -5) = 0 Reorder the terms: -15 + -7a + 2a2 + (-5 + 4a)(-5 + a) = 0 Multiply (-5 + 4a) * (-5 + a) -15 + -7a + 2a2 + (-5(-5 + a) + 4a * (-5 + a)) = 0 -15 + -7a + 2a2 + ((-5 * -5 + a * -5) + 4a * (-5 + a)) = 0 -15 + -7a + 2a2 + ((25 + -5a) + 4a * (-5 + a)) = 0 -15 + -7a + 2a2 + (25 + -5a + (-5 * 4a + a * 4a)) = 0 -15 + -7a + 2a2 + (25 + -5a + (-20a + 4a2)) = 0 Combine like terms: -5a + -20a = -25a -15 + -7a + 2a2 + (25 + -25a + 4a2) = 0 Reorder the terms: -15 + 25 + -7a + -25a + 2a2 + 4a2 = 0 Combine like terms: -15 + 25 = 10 10 + -7a + -25a + 2a2 + 4a2 = 0 Combine like terms: -7a + -25a = -32a 10 + -32a + 2a2 + 4a2 = 0 Combine like terms: 2a2 + 4a2 = 6a2 10 + -32a + 6a2 = 0 Solving 10 + -32a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -16a + 3a2) = 0 Factor a trinomial. 2((1 + -3a)(5 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {0.3333333333, 5}
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