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Simplifying 12(3y + -3) + 5(y + -1)(3y + -3) = -24y + 24 Reorder the terms: 12(-3 + 3y) + 5(y + -1)(3y + -3) = -24y + 24 (-3 * 12 + 3y * 12) + 5(y + -1)(3y + -3) = -24y + 24 (-36 + 36y) + 5(y + -1)(3y + -3) = -24y + 24 Reorder the terms: -36 + 36y + 5(-1 + y)(3y + -3) = -24y + 24 Reorder the terms: -36 + 36y + 5(-1 + y)(-3 + 3y) = -24y + 24 Multiply (-1 + y) * (-3 + 3y) -36 + 36y + 5(-1(-3 + 3y) + y(-3 + 3y)) = -24y + 24 -36 + 36y + 5((-3 * -1 + 3y * -1) + y(-3 + 3y)) = -24y + 24 -36 + 36y + 5((3 + -3y) + y(-3 + 3y)) = -24y + 24 -36 + 36y + 5(3 + -3y + (-3 * y + 3y * y)) = -24y + 24 -36 + 36y + 5(3 + -3y + (-3y + 3y2)) = -24y + 24 Combine like terms: -3y + -3y = -6y -36 + 36y + 5(3 + -6y + 3y2) = -24y + 24 -36 + 36y + (3 * 5 + -6y * 5 + 3y2 * 5) = -24y + 24 -36 + 36y + (15 + -30y + 15y2) = -24y + 24 Reorder the terms: -36 + 15 + 36y + -30y + 15y2 = -24y + 24 Combine like terms: -36 + 15 = -21 -21 + 36y + -30y + 15y2 = -24y + 24 Combine like terms: 36y + -30y = 6y -21 + 6y + 15y2 = -24y + 24 Reorder the terms: -21 + 6y + 15y2 = 24 + -24y Solving -21 + 6y + 15y2 = 24 + -24y Solving for variable 'y'. Reorder the terms: -21 + -24 + 6y + 24y + 15y2 = 24 + -24y + -24 + 24y Combine like terms: -21 + -24 = -45 -45 + 6y + 24y + 15y2 = 24 + -24y + -24 + 24y Combine like terms: 6y + 24y = 30y -45 + 30y + 15y2 = 24 + -24y + -24 + 24y Reorder the terms: -45 + 30y + 15y2 = 24 + -24 + -24y + 24y Combine like terms: 24 + -24 = 0 -45 + 30y + 15y2 = 0 + -24y + 24y -45 + 30y + 15y2 = -24y + 24y Combine like terms: -24y + 24y = 0 -45 + 30y + 15y2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-3 + 2y + y2) = 0 Factor a trinomial. 15((-3 + -1y)(1 + -1y)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {-3, 1}
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