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Simplifying [9(q + 5) + -17] + [3(q + -3) + 5] = 0 Reorder the terms: [9(5 + q) + -17] + [3(q + -3) + 5] = 0 [(5 * 9 + q * 9) + -17] + [3(q + -3) + 5] = 0 [(45 + 9q) + -17] + [3(q + -3) + 5] = 0 Reorder the terms: [45 + -17 + 9q] + [3(q + -3) + 5] = 0 Combine like terms: 45 + -17 = 28 [28 + 9q] + [3(q + -3) + 5] = 0 Remove brackets around [28 + 9q] 28 + 9q + [3(q + -3) + 5] = 0 Reorder the terms: 28 + 9q + [3(-3 + q) + 5] = 0 28 + 9q + [(-3 * 3 + q * 3) + 5] = 0 28 + 9q + [(-9 + 3q) + 5] = 0 Reorder the terms: 28 + 9q + [-9 + 5 + 3q] = 0 Combine like terms: -9 + 5 = -4 28 + 9q + [-4 + 3q] = 0 Remove brackets around [-4 + 3q] 28 + 9q + -4 + 3q = 0 Reorder the terms: 28 + -4 + 9q + 3q = 0 Combine like terms: 28 + -4 = 24 24 + 9q + 3q = 0 Combine like terms: 9q + 3q = 12q 24 + 12q = 0 Solving 24 + 12q = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + 12q = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12q = 0 + -24 12q = 0 + -24 Combine like terms: 0 + -24 = -24 12q = -24 Divide each side by '12'. q = -2 Simplifying q = -2
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