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Simplifying -6(y + 3) + 3(4y + -5) = 5(y + -6) + 12 Reorder the terms: -6(3 + y) + 3(4y + -5) = 5(y + -6) + 12 (3 * -6 + y * -6) + 3(4y + -5) = 5(y + -6) + 12 (-18 + -6y) + 3(4y + -5) = 5(y + -6) + 12 Reorder the terms: -18 + -6y + 3(-5 + 4y) = 5(y + -6) + 12 -18 + -6y + (-5 * 3 + 4y * 3) = 5(y + -6) + 12 -18 + -6y + (-15 + 12y) = 5(y + -6) + 12 Reorder the terms: -18 + -15 + -6y + 12y = 5(y + -6) + 12 Combine like terms: -18 + -15 = -33 -33 + -6y + 12y = 5(y + -6) + 12 Combine like terms: -6y + 12y = 6y -33 + 6y = 5(y + -6) + 12 Reorder the terms: -33 + 6y = 5(-6 + y) + 12 -33 + 6y = (-6 * 5 + y * 5) + 12 -33 + 6y = (-30 + 5y) + 12 Reorder the terms: -33 + 6y = -30 + 12 + 5y Combine like terms: -30 + 12 = -18 -33 + 6y = -18 + 5y Solving -33 + 6y = -18 + 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. -33 + 6y + -5y = -18 + 5y + -5y Combine like terms: 6y + -5y = 1y -33 + 1y = -18 + 5y + -5y Combine like terms: 5y + -5y = 0 -33 + 1y = -18 + 0 -33 + 1y = -18 Add '33' to each side of the equation. -33 + 33 + 1y = -18 + 33 Combine like terms: -33 + 33 = 0 0 + 1y = -18 + 33 1y = -18 + 33 Combine like terms: -18 + 33 = 15 1y = 15 Divide each side by '1'. y = 15 Simplifying y = 15
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