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Simplifying y(3 + -5y) + 2y2 = 9 + -1y2 + -2y(y + -3) (3 * y + -5y * y) + 2y2 = 9 + -1y2 + -2y(y + -3) (3y + -5y2) + 2y2 = 9 + -1y2 + -2y(y + -3) Combine like terms: -5y2 + 2y2 = -3y2 3y + -3y2 = 9 + -1y2 + -2y(y + -3) Reorder the terms: 3y + -3y2 = 9 + -1y2 + -2y(-3 + y) 3y + -3y2 = 9 + -1y2 + (-3 * -2y + y * -2y) 3y + -3y2 = 9 + -1y2 + (6y + -2y2) Reorder the terms: 3y + -3y2 = 9 + 6y + -1y2 + -2y2 Combine like terms: -1y2 + -2y2 = -3y2 3y + -3y2 = 9 + 6y + -3y2 Add '3y2' to each side of the equation. 3y + -3y2 + 3y2 = 9 + 6y + -3y2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 3y + 0 = 9 + 6y + -3y2 + 3y2 3y = 9 + 6y + -3y2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 3y = 9 + 6y + 0 3y = 9 + 6y Solving 3y = 9 + 6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6y' to each side of the equation. 3y + -6y = 9 + 6y + -6y Combine like terms: 3y + -6y = -3y -3y = 9 + 6y + -6y Combine like terms: 6y + -6y = 0 -3y = 9 + 0 -3y = 9 Divide each side by '-3'. y = -3 Simplifying y = -3
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