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Simplifying (y + 3)(y + -4) = y(y + -5) + 2(y + 6) Reorder the terms: (3 + y)(y + -4) = y(y + -5) + 2(y + 6) Reorder the terms: (3 + y)(-4 + y) = y(y + -5) + 2(y + 6) Multiply (3 + y) * (-4 + y) (3(-4 + y) + y(-4 + y)) = y(y + -5) + 2(y + 6) ((-4 * 3 + y * 3) + y(-4 + y)) = y(y + -5) + 2(y + 6) ((-12 + 3y) + y(-4 + y)) = y(y + -5) + 2(y + 6) (-12 + 3y + (-4 * y + y * y)) = y(y + -5) + 2(y + 6) (-12 + 3y + (-4y + y2)) = y(y + -5) + 2(y + 6) Combine like terms: 3y + -4y = -1y (-12 + -1y + y2) = y(y + -5) + 2(y + 6) Reorder the terms: -12 + -1y + y2 = y(-5 + y) + 2(y + 6) -12 + -1y + y2 = (-5 * y + y * y) + 2(y + 6) -12 + -1y + y2 = (-5y + y2) + 2(y + 6) Reorder the terms: -12 + -1y + y2 = -5y + y2 + 2(6 + y) -12 + -1y + y2 = -5y + y2 + (6 * 2 + y * 2) -12 + -1y + y2 = -5y + y2 + (12 + 2y) Reorder the terms: -12 + -1y + y2 = 12 + -5y + 2y + y2 Combine like terms: -5y + 2y = -3y -12 + -1y + y2 = 12 + -3y + y2 Add '-1y2' to each side of the equation. -12 + -1y + y2 + -1y2 = 12 + -3y + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + -1y + 0 = 12 + -3y + y2 + -1y2 -12 + -1y = 12 + -3y + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + -1y = 12 + -3y + 0 -12 + -1y = 12 + -3y Solving -12 + -1y = 12 + -3y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3y' to each side of the equation. -12 + -1y + 3y = 12 + -3y + 3y Combine like terms: -1y + 3y = 2y -12 + 2y = 12 + -3y + 3y Combine like terms: -3y + 3y = 0 -12 + 2y = 12 + 0 -12 + 2y = 12 Add '12' to each side of the equation. -12 + 12 + 2y = 12 + 12 Combine like terms: -12 + 12 = 0 0 + 2y = 12 + 12 2y = 12 + 12 Combine like terms: 12 + 12 = 24 2y = 24 Divide each side by '2'. y = 12 Simplifying y = 12
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