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Simplifying (y + -1)(y + 2) = (y + -6)(y + -4) + 7 Reorder the terms: (-1 + y)(y + 2) = (y + -6)(y + -4) + 7 Reorder the terms: (-1 + y)(2 + y) = (y + -6)(y + -4) + 7 Multiply (-1 + y) * (2 + y) (-1(2 + y) + y(2 + y)) = (y + -6)(y + -4) + 7 ((2 * -1 + y * -1) + y(2 + y)) = (y + -6)(y + -4) + 7 ((-2 + -1y) + y(2 + y)) = (y + -6)(y + -4) + 7 (-2 + -1y + (2 * y + y * y)) = (y + -6)(y + -4) + 7 (-2 + -1y + (2y + y2)) = (y + -6)(y + -4) + 7 Combine like terms: -1y + 2y = 1y (-2 + 1y + y2) = (y + -6)(y + -4) + 7 Reorder the terms: -2 + 1y + y2 = (-6 + y)(y + -4) + 7 Reorder the terms: -2 + 1y + y2 = (-6 + y)(-4 + y) + 7 Multiply (-6 + y) * (-4 + y) -2 + 1y + y2 = (-6(-4 + y) + y(-4 + y)) + 7 -2 + 1y + y2 = ((-4 * -6 + y * -6) + y(-4 + y)) + 7 -2 + 1y + y2 = ((24 + -6y) + y(-4 + y)) + 7 -2 + 1y + y2 = (24 + -6y + (-4 * y + y * y)) + 7 -2 + 1y + y2 = (24 + -6y + (-4y + y2)) + 7 Combine like terms: -6y + -4y = -10y -2 + 1y + y2 = (24 + -10y + y2) + 7 Reorder the terms: -2 + 1y + y2 = 24 + 7 + -10y + y2 Combine like terms: 24 + 7 = 31 -2 + 1y + y2 = 31 + -10y + y2 Add '-1y2' to each side of the equation. -2 + 1y + y2 + -1y2 = 31 + -10y + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -2 + 1y + 0 = 31 + -10y + y2 + -1y2 -2 + 1y = 31 + -10y + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -2 + 1y = 31 + -10y + 0 -2 + 1y = 31 + -10y Solving -2 + 1y = 31 + -10y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10y' to each side of the equation. -2 + 1y + 10y = 31 + -10y + 10y Combine like terms: 1y + 10y = 11y -2 + 11y = 31 + -10y + 10y Combine like terms: -10y + 10y = 0 -2 + 11y = 31 + 0 -2 + 11y = 31 Add '2' to each side of the equation. -2 + 2 + 11y = 31 + 2 Combine like terms: -2 + 2 = 0 0 + 11y = 31 + 2 11y = 31 + 2 Combine like terms: 31 + 2 = 33 11y = 33 Divide each side by '11'. y = 3 Simplifying y = 3
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