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Simplifying (y + 3)(y + 5) = y(y + 11) Reorder the terms: (3 + y)(y + 5) = y(y + 11) Reorder the terms: (3 + y)(5 + y) = y(y + 11) Multiply (3 + y) * (5 + y) (3(5 + y) + y(5 + y)) = y(y + 11) ((5 * 3 + y * 3) + y(5 + y)) = y(y + 11) ((15 + 3y) + y(5 + y)) = y(y + 11) (15 + 3y + (5 * y + y * y)) = y(y + 11) (15 + 3y + (5y + y2)) = y(y + 11) Combine like terms: 3y + 5y = 8y (15 + 8y + y2) = y(y + 11) Reorder the terms: 15 + 8y + y2 = y(11 + y) 15 + 8y + y2 = (11 * y + y * y) 15 + 8y + y2 = (11y + y2) Add '-1y2' to each side of the equation. 15 + 8y + y2 + -1y2 = 11y + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 15 + 8y + 0 = 11y + y2 + -1y2 15 + 8y = 11y + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 15 + 8y = 11y + 0 15 + 8y = 11y Solving 15 + 8y = 11y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-11y' to each side of the equation. 15 + 8y + -11y = 11y + -11y Combine like terms: 8y + -11y = -3y 15 + -3y = 11y + -11y Combine like terms: 11y + -11y = 0 15 + -3y = 0 Add '-15' to each side of the equation. 15 + -15 + -3y = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -3y = 0 + -15 -3y = 0 + -15 Combine like terms: 0 + -15 = -15 -3y = -15 Divide each side by '-3'. y = 5 Simplifying y = 5
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