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Simplifying y + -3y(1 + -12y) = 11 + -1(5 + -6y)(6y + 5) y + (1 * -3y + -12y * -3y) = 11 + -1(5 + -6y)(6y + 5) y + (-3y + 36y2) = 11 + -1(5 + -6y)(6y + 5) Combine like terms: y + -3y = -2y -2y + 36y2 = 11 + -1(5 + -6y)(6y + 5) Reorder the terms: -2y + 36y2 = 11 + -1(5 + -6y)(5 + 6y) Multiply (5 + -6y) * (5 + 6y) -2y + 36y2 = 11 + -1(5(5 + 6y) + -6y * (5 + 6y)) -2y + 36y2 = 11 + -1((5 * 5 + 6y * 5) + -6y * (5 + 6y)) -2y + 36y2 = 11 + -1((25 + 30y) + -6y * (5 + 6y)) -2y + 36y2 = 11 + -1(25 + 30y + (5 * -6y + 6y * -6y)) -2y + 36y2 = 11 + -1(25 + 30y + (-30y + -36y2)) Combine like terms: 30y + -30y = 0 -2y + 36y2 = 11 + -1(25 + 0 + -36y2) -2y + 36y2 = 11 + -1(25 + -36y2) -2y + 36y2 = 11 + (25 * -1 + -36y2 * -1) -2y + 36y2 = 11 + (-25 + 36y2) Combine like terms: 11 + -25 = -14 -2y + 36y2 = -14 + 36y2 Add '-36y2' to each side of the equation. -2y + 36y2 + -36y2 = -14 + 36y2 + -36y2 Combine like terms: 36y2 + -36y2 = 0 -2y + 0 = -14 + 36y2 + -36y2 -2y = -14 + 36y2 + -36y2 Combine like terms: 36y2 + -36y2 = 0 -2y = -14 + 0 -2y = -14 Solving -2y = -14 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Divide each side by '-2'. y = 7 Simplifying y = 7
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