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Simplifying 5[3(6 + -1y) + -4(8 + 3y)] + -132 = -6[5(6 + 3y) + -3] 5[(6 * 3 + -1y * 3) + -4(8 + 3y)] + -132 = -6[5(6 + 3y) + -3] 5[(18 + -3y) + -4(8 + 3y)] + -132 = -6[5(6 + 3y) + -3] 5[18 + -3y + (8 * -4 + 3y * -4)] + -132 = -6[5(6 + 3y) + -3] 5[18 + -3y + (-32 + -12y)] + -132 = -6[5(6 + 3y) + -3] Reorder the terms: 5[18 + -32 + -3y + -12y] + -132 = -6[5(6 + 3y) + -3] Combine like terms: 18 + -32 = -14 5[-14 + -3y + -12y] + -132 = -6[5(6 + 3y) + -3] Combine like terms: -3y + -12y = -15y 5[-14 + -15y] + -132 = -6[5(6 + 3y) + -3] [-14 * 5 + -15y * 5] + -132 = -6[5(6 + 3y) + -3] [-70 + -75y] + -132 = -6[5(6 + 3y) + -3] Reorder the terms: -70 + -132 + -75y = -6[5(6 + 3y) + -3] Combine like terms: -70 + -132 = -202 -202 + -75y = -6[5(6 + 3y) + -3] -202 + -75y = -6[(6 * 5 + 3y * 5) + -3] -202 + -75y = -6[(30 + 15y) + -3] Reorder the terms: -202 + -75y = -6[30 + -3 + 15y] Combine like terms: 30 + -3 = 27 -202 + -75y = -6[27 + 15y] -202 + -75y = [27 * -6 + 15y * -6] -202 + -75y = [-162 + -90y] Solving -202 + -75y = -162 + -90y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '90y' to each side of the equation. -202 + -75y + 90y = -162 + -90y + 90y Combine like terms: -75y + 90y = 15y -202 + 15y = -162 + -90y + 90y Combine like terms: -90y + 90y = 0 -202 + 15y = -162 + 0 -202 + 15y = -162 Add '202' to each side of the equation. -202 + 202 + 15y = -162 + 202 Combine like terms: -202 + 202 = 0 0 + 15y = -162 + 202 15y = -162 + 202 Combine like terms: -162 + 202 = 40 15y = 40 Divide each side by '15'. y = 2.666666667 Simplifying y = 2.666666667
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