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Simplifying -6(y + 3) + 4(3y + -4) = 5(y + -5) + 12 Reorder the terms: -6(3 + y) + 4(3y + -4) = 5(y + -5) + 12 (3 * -6 + y * -6) + 4(3y + -4) = 5(y + -5) + 12 (-18 + -6y) + 4(3y + -4) = 5(y + -5) + 12 Reorder the terms: -18 + -6y + 4(-4 + 3y) = 5(y + -5) + 12 -18 + -6y + (-4 * 4 + 3y * 4) = 5(y + -5) + 12 -18 + -6y + (-16 + 12y) = 5(y + -5) + 12 Reorder the terms: -18 + -16 + -6y + 12y = 5(y + -5) + 12 Combine like terms: -18 + -16 = -34 -34 + -6y + 12y = 5(y + -5) + 12 Combine like terms: -6y + 12y = 6y -34 + 6y = 5(y + -5) + 12 Reorder the terms: -34 + 6y = 5(-5 + y) + 12 -34 + 6y = (-5 * 5 + y * 5) + 12 -34 + 6y = (-25 + 5y) + 12 Reorder the terms: -34 + 6y = -25 + 12 + 5y Combine like terms: -25 + 12 = -13 -34 + 6y = -13 + 5y Solving -34 + 6y = -13 + 5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5y' to each side of the equation. -34 + 6y + -5y = -13 + 5y + -5y Combine like terms: 6y + -5y = 1y -34 + 1y = -13 + 5y + -5y Combine like terms: 5y + -5y = 0 -34 + 1y = -13 + 0 -34 + 1y = -13 Add '34' to each side of the equation. -34 + 34 + 1y = -13 + 34 Combine like terms: -34 + 34 = 0 0 + 1y = -13 + 34 1y = -13 + 34 Combine like terms: -13 + 34 = 21 1y = 21 Divide each side by '1'. y = 21 Simplifying y = 21
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