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Simplifying [9(y + 5) + -16] + [3(y + -2) + 1] = 0 Reorder the terms: [9(5 + y) + -16] + [3(y + -2) + 1] = 0 [(5 * 9 + y * 9) + -16] + [3(y + -2) + 1] = 0 [(45 + 9y) + -16] + [3(y + -2) + 1] = 0 Reorder the terms: [45 + -16 + 9y] + [3(y + -2) + 1] = 0 Combine like terms: 45 + -16 = 29 [29 + 9y] + [3(y + -2) + 1] = 0 Remove brackets around [29 + 9y] 29 + 9y + [3(y + -2) + 1] = 0 Reorder the terms: 29 + 9y + [3(-2 + y) + 1] = 0 29 + 9y + [(-2 * 3 + y * 3) + 1] = 0 29 + 9y + [(-6 + 3y) + 1] = 0 Reorder the terms: 29 + 9y + [-6 + 1 + 3y] = 0 Combine like terms: -6 + 1 = -5 29 + 9y + [-5 + 3y] = 0 Remove brackets around [-5 + 3y] 29 + 9y + -5 + 3y = 0 Reorder the terms: 29 + -5 + 9y + 3y = 0 Combine like terms: 29 + -5 = 24 24 + 9y + 3y = 0 Combine like terms: 9y + 3y = 12y 24 + 12y = 0 Solving 24 + 12y = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + 12y = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12y = 0 + -24 12y = 0 + -24 Combine like terms: 0 + -24 = -24 12y = -24 Divide each side by '12'. y = -2 Simplifying y = -2
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