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Simplifying 5((3(a + -5) + 16) + -1(3(4a + -2) + 4)) = 0 Reorder the terms: 5((3(-5 + a) + 16) + -1(3(4a + -2) + 4)) = 0 5(((-5 * 3 + a * 3) + 16) + -1(3(4a + -2) + 4)) = 0 5(((-15 + 3a) + 16) + -1(3(4a + -2) + 4)) = 0 Reorder the terms: 5((-15 + 16 + 3a) + -1(3(4a + -2) + 4)) = 0 Combine like terms: -15 + 16 = 1 5((1 + 3a) + -1(3(4a + -2) + 4)) = 0 Remove parenthesis around (1 + 3a) 5(1 + 3a + -1(3(4a + -2) + 4)) = 0 Reorder the terms: 5(1 + 3a + -1(3(-2 + 4a) + 4)) = 0 5(1 + 3a + -1((-2 * 3 + 4a * 3) + 4)) = 0 5(1 + 3a + -1((-6 + 12a) + 4)) = 0 Reorder the terms: 5(1 + 3a + -1(-6 + 4 + 12a)) = 0 Combine like terms: -6 + 4 = -2 5(1 + 3a + -1(-2 + 12a)) = 0 5(1 + 3a + (-2 * -1 + 12a * -1)) = 0 5(1 + 3a + (2 + -12a)) = 0 Reorder the terms: 5(1 + 2 + 3a + -12a) = 0 Combine like terms: 1 + 2 = 3 5(3 + 3a + -12a) = 0 Combine like terms: 3a + -12a = -9a 5(3 + -9a) = 0 (3 * 5 + -9a * 5) = 0 (15 + -45a) = 0 Solving 15 + -45a = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -45a = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -45a = 0 + -15 -45a = 0 + -15 Combine like terms: 0 + -15 = -15 -45a = -15 Divide each side by '-45'. a = 0.3333333333 Simplifying a = 0.3333333333
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