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Simplifying 0 = [4(y + 8) + -2(1 + -1y)] + -1[-7 + -1(2y + 19)] Reorder the terms: 0 = [4(8 + y) + -2(1 + -1y)] + -1[-7 + -1(2y + 19)] 0 = [(8 * 4 + y * 4) + -2(1 + -1y)] + -1[-7 + -1(2y + 19)] 0 = [(32 + 4y) + -2(1 + -1y)] + -1[-7 + -1(2y + 19)] 0 = [32 + 4y + (1 * -2 + -1y * -2)] + -1[-7 + -1(2y + 19)] 0 = [32 + 4y + (-2 + 2y)] + -1[-7 + -1(2y + 19)] Reorder the terms: 0 = [32 + -2 + 4y + 2y] + -1[-7 + -1(2y + 19)] Combine like terms: 32 + -2 = 30 0 = [30 + 4y + 2y] + -1[-7 + -1(2y + 19)] Combine like terms: 4y + 2y = 6y 0 = [30 + 6y] + -1[-7 + -1(2y + 19)] Remove brackets around [30 + 6y] 0 = 30 + 6y + -1[-7 + -1(2y + 19)] Reorder the terms: 0 = 30 + 6y + -1[-7 + -1(19 + 2y)] 0 = 30 + 6y + -1[-7 + (19 * -1 + 2y * -1)] 0 = 30 + 6y + -1[-7 + (-19 + -2y)] Combine like terms: -7 + -19 = -26 0 = 30 + 6y + -1[-26 + -2y] 0 = 30 + 6y + [-26 * -1 + -2y * -1] 0 = 30 + 6y + [26 + 2y] Reorder the terms: 0 = 30 + 26 + 6y + 2y Combine like terms: 30 + 26 = 56 0 = 56 + 6y + 2y Combine like terms: 6y + 2y = 8y 0 = 56 + 8y Solving 0 = 56 + 8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8y' to each side of the equation. 0 + -8y = 56 + 8y + -8y Remove the zero: -8y = 56 + 8y + -8y Combine like terms: 8y + -8y = 0 -8y = 56 + 0 -8y = 56 Divide each side by '-8'. y = -7 Simplifying y = -7
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