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Simplifying (y + 12)(y + -3) + -1y(y + 5) = 24 Reorder the terms: (12 + y)(y + -3) + -1y(y + 5) = 24 Reorder the terms: (12 + y)(-3 + y) + -1y(y + 5) = 24 Multiply (12 + y) * (-3 + y) (12(-3 + y) + y(-3 + y)) + -1y(y + 5) = 24 ((-3 * 12 + y * 12) + y(-3 + y)) + -1y(y + 5) = 24 ((-36 + 12y) + y(-3 + y)) + -1y(y + 5) = 24 (-36 + 12y + (-3 * y + y * y)) + -1y(y + 5) = 24 (-36 + 12y + (-3y + y2)) + -1y(y + 5) = 24 Combine like terms: 12y + -3y = 9y (-36 + 9y + y2) + -1y(y + 5) = 24 Reorder the terms: -36 + 9y + y2 + -1y(5 + y) = 24 -36 + 9y + y2 + (5 * -1y + y * -1y) = 24 -36 + 9y + y2 + (-5y + -1y2) = 24 Reorder the terms: -36 + 9y + -5y + y2 + -1y2 = 24 Combine like terms: 9y + -5y = 4y -36 + 4y + y2 + -1y2 = 24 Combine like terms: y2 + -1y2 = 0 -36 + 4y + 0 = 24 -36 + 4y = 24 Solving -36 + 4y = 24 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + 4y = 24 + 36 Combine like terms: -36 + 36 = 0 0 + 4y = 24 + 36 4y = 24 + 36 Combine like terms: 24 + 36 = 60 4y = 60 Divide each side by '4'. y = 15 Simplifying y = 15
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