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Simplifying 15(20 + -5y + -23z) + 78(3 + -5z) + 360z = 309 (20 * 15 + -5y * 15 + -23z * 15) + 78(3 + -5z) + 360z = 309 (300 + -75y + -345z) + 78(3 + -5z) + 360z = 309 300 + -75y + -345z + (3 * 78 + -5z * 78) + 360z = 309 300 + -75y + -345z + (234 + -390z) + 360z = 309 Reorder the terms: 300 + 234 + -75y + -345z + -390z + 360z = 309 Combine like terms: 300 + 234 = 534 534 + -75y + -345z + -390z + 360z = 309 Combine like terms: -345z + -390z = -735z 534 + -75y + -735z + 360z = 309 Combine like terms: -735z + 360z = -375z 534 + -75y + -375z = 309 Solving 534 + -75y + -375z = 309 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-534' to each side of the equation. 534 + -75y + -534 + -375z = 309 + -534 Reorder the terms: 534 + -534 + -75y + -375z = 309 + -534 Combine like terms: 534 + -534 = 0 0 + -75y + -375z = 309 + -534 -75y + -375z = 309 + -534 Combine like terms: 309 + -534 = -225 -75y + -375z = -225 Add '375z' to each side of the equation. -75y + -375z + 375z = -225 + 375z Combine like terms: -375z + 375z = 0 -75y + 0 = -225 + 375z -75y = -225 + 375z Divide each side by '-75'. y = 3 + -5z Simplifying y = 3 + -5z
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