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Simplifying 3((3(q + -4) + 17) + -1(3(4q + -2) + 1)) = 0 Reorder the terms: 3((3(-4 + q) + 17) + -1(3(4q + -2) + 1)) = 0 3(((-4 * 3 + q * 3) + 17) + -1(3(4q + -2) + 1)) = 0 3(((-12 + 3q) + 17) + -1(3(4q + -2) + 1)) = 0 Reorder the terms: 3((-12 + 17 + 3q) + -1(3(4q + -2) + 1)) = 0 Combine like terms: -12 + 17 = 5 3((5 + 3q) + -1(3(4q + -2) + 1)) = 0 Remove parenthesis around (5 + 3q) 3(5 + 3q + -1(3(4q + -2) + 1)) = 0 Reorder the terms: 3(5 + 3q + -1(3(-2 + 4q) + 1)) = 0 3(5 + 3q + -1((-2 * 3 + 4q * 3) + 1)) = 0 3(5 + 3q + -1((-6 + 12q) + 1)) = 0 Reorder the terms: 3(5 + 3q + -1(-6 + 1 + 12q)) = 0 Combine like terms: -6 + 1 = -5 3(5 + 3q + -1(-5 + 12q)) = 0 3(5 + 3q + (-5 * -1 + 12q * -1)) = 0 3(5 + 3q + (5 + -12q)) = 0 Reorder the terms: 3(5 + 5 + 3q + -12q) = 0 Combine like terms: 5 + 5 = 10 3(10 + 3q + -12q) = 0 Combine like terms: 3q + -12q = -9q 3(10 + -9q) = 0 (10 * 3 + -9q * 3) = 0 (30 + -27q) = 0 Solving 30 + -27q = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -27q = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -27q = 0 + -30 -27q = 0 + -30 Combine like terms: 0 + -30 = -30 -27q = -30 Divide each side by '-27'. q = 1.111111111 Simplifying q = 1.111111111
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