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Simplifying 3(4y + 2) + -6(3y + 4) = 5(y + -7) + -12(y + -18) Reorder the terms: 3(2 + 4y) + -6(3y + 4) = 5(y + -7) + -12(y + -18) (2 * 3 + 4y * 3) + -6(3y + 4) = 5(y + -7) + -12(y + -18) (6 + 12y) + -6(3y + 4) = 5(y + -7) + -12(y + -18) Reorder the terms: 6 + 12y + -6(4 + 3y) = 5(y + -7) + -12(y + -18) 6 + 12y + (4 * -6 + 3y * -6) = 5(y + -7) + -12(y + -18) 6 + 12y + (-24 + -18y) = 5(y + -7) + -12(y + -18) Reorder the terms: 6 + -24 + 12y + -18y = 5(y + -7) + -12(y + -18) Combine like terms: 6 + -24 = -18 -18 + 12y + -18y = 5(y + -7) + -12(y + -18) Combine like terms: 12y + -18y = -6y -18 + -6y = 5(y + -7) + -12(y + -18) Reorder the terms: -18 + -6y = 5(-7 + y) + -12(y + -18) -18 + -6y = (-7 * 5 + y * 5) + -12(y + -18) -18 + -6y = (-35 + 5y) + -12(y + -18) Reorder the terms: -18 + -6y = -35 + 5y + -12(-18 + y) -18 + -6y = -35 + 5y + (-18 * -12 + y * -12) -18 + -6y = -35 + 5y + (216 + -12y) Reorder the terms: -18 + -6y = -35 + 216 + 5y + -12y Combine like terms: -35 + 216 = 181 -18 + -6y = 181 + 5y + -12y Combine like terms: 5y + -12y = -7y -18 + -6y = 181 + -7y Solving -18 + -6y = 181 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. -18 + -6y + 7y = 181 + -7y + 7y Combine like terms: -6y + 7y = 1y -18 + 1y = 181 + -7y + 7y Combine like terms: -7y + 7y = 0 -18 + 1y = 181 + 0 -18 + 1y = 181 Add '18' to each side of the equation. -18 + 18 + 1y = 181 + 18 Combine like terms: -18 + 18 = 0 0 + 1y = 181 + 18 1y = 181 + 18 Combine like terms: 181 + 18 = 199 1y = 199 Divide each side by '1'. y = 199 Simplifying y = 199
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