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Simplifying 5(y + -5)(y + -3) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) Reorder the terms: 5(-5 + y)(y + -3) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) Reorder the terms: 5(-5 + y)(-3 + y) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) Multiply (-5 + y) * (-3 + y) 5(-5(-3 + y) + y(-3 + y)) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) 5((-3 * -5 + y * -5) + y(-3 + y)) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) 5((15 + -5y) + y(-3 + y)) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) 5(15 + -5y + (-3 * y + y * y)) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) 5(15 + -5y + (-3y + y2)) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) Combine like terms: -5y + -3y = -8y 5(15 + -8y + y2) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) (15 * 5 + -8y * 5 + y2 * 5) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) (75 + -40y + 5y2) + 4(y + 4)(y + 3) = 9(y + 4)(y + -5) Reorder the terms: 75 + -40y + 5y2 + 4(4 + y)(y + 3) = 9(y + 4)(y + -5) Reorder the terms: 75 + -40y + 5y2 + 4(4 + y)(3 + y) = 9(y + 4)(y + -5) Multiply (4 + y) * (3 + y) 75 + -40y + 5y2 + 4(4(3 + y) + y(3 + y)) = 9(y + 4)(y + -5) 75 + -40y + 5y2 + 4((3 * 4 + y * 4) + y(3 + y)) = 9(y + 4)(y + -5) 75 + -40y + 5y2 + 4((12 + 4y) + y(3 + y)) = 9(y + 4)(y + -5) 75 + -40y + 5y2 + 4(12 + 4y + (3 * y + y * y)) = 9(y + 4)(y + -5) 75 + -40y + 5y2 + 4(12 + 4y + (3y + y2)) = 9(y + 4)(y + -5) Combine like terms: 4y + 3y = 7y 75 + -40y + 5y2 + 4(12 + 7y + y2) = 9(y + 4)(y + -5) 75 + -40y + 5y2 + (12 * 4 + 7y * 4 + y2 * 4) = 9(y + 4)(y + -5) 75 + -40y + 5y2 + (48 + 28y + 4y2) = 9(y + 4)(y + -5) Reorder the terms: 75 + 48 + -40y + 28y + 5y2 + 4y2 = 9(y + 4)(y + -5) Combine like terms: 75 + 48 = 123 123 + -40y + 28y + 5y2 + 4y2 = 9(y + 4)(y + -5) Combine like terms: -40y + 28y = -12y 123 + -12y + 5y2 + 4y2 = 9(y + 4)(y + -5) Combine like terms: 5y2 + 4y2 = 9y2 123 + -12y + 9y2 = 9(y + 4)(y + -5) Reorder the terms: 123 + -12y + 9y2 = 9(4 + y)(y + -5) Reorder the terms: 123 + -12y + 9y2 = 9(4 + y)(-5 + y) Multiply (4 + y) * (-5 + y) 123 + -12y + 9y2 = 9(4(-5 + y) + y(-5 + y)) 123 + -12y + 9y2 = 9((-5 * 4 + y * 4) + y(-5 + y)) 123 + -12y + 9y2 = 9((-20 + 4y) + y(-5 + y)) 123 + -12y + 9y2 = 9(-20 + 4y + (-5 * y + y * y)) 123 + -12y + 9y2 = 9(-20 + 4y + (-5y + y2)) Combine like terms: 4y + -5y = -1y 123 + -12y + 9y2 = 9(-20 + -1y + y2) 123 + -12y + 9y2 = (-20 * 9 + -1y * 9 + y2 * 9) 123 + -12y + 9y2 = (-180 + -9y + 9y2) Add '-9y2' to each side of the equation. 123 + -12y + 9y2 + -9y2 = -180 + -9y + 9y2 + -9y2 Combine like terms: 9y2 + -9y2 = 0 123 + -12y + 0 = -180 + -9y + 9y2 + -9y2 123 + -12y = -180 + -9y + 9y2 + -9y2 Combine like terms: 9y2 + -9y2 = 0 123 + -12y = -180 + -9y + 0 123 + -12y = -180 + -9y Solving 123 + -12y = -180 + -9y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9y' to each side of the equation. 123 + -12y + 9y = -180 + -9y + 9y Combine like terms: -12y + 9y = -3y 123 + -3y = -180 + -9y + 9y Combine like terms: -9y + 9y = 0 123 + -3y = -180 + 0 123 + -3y = -180 Add '-123' to each side of the equation. 123 + -123 + -3y = -180 + -123 Combine like terms: 123 + -123 = 0 0 + -3y = -180 + -123 -3y = -180 + -123 Combine like terms: -180 + -123 = -303 -3y = -303 Divide each side by '-3'. y = 101 Simplifying y = 101
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