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Simplifying (3y + -4)(3y + -2) = -1(6y + -5) Reorder the terms: (-4 + 3y)(3y + -2) = -1(6y + -5) Reorder the terms: (-4 + 3y)(-2 + 3y) = -1(6y + -5) Multiply (-4 + 3y) * (-2 + 3y) (-4(-2 + 3y) + 3y * (-2 + 3y)) = -1(6y + -5) ((-2 * -4 + 3y * -4) + 3y * (-2 + 3y)) = -1(6y + -5) ((8 + -12y) + 3y * (-2 + 3y)) = -1(6y + -5) (8 + -12y + (-2 * 3y + 3y * 3y)) = -1(6y + -5) (8 + -12y + (-6y + 9y2)) = -1(6y + -5) Combine like terms: -12y + -6y = -18y (8 + -18y + 9y2) = -1(6y + -5) Reorder the terms: 8 + -18y + 9y2 = -1(-5 + 6y) 8 + -18y + 9y2 = (-5 * -1 + 6y * -1) 8 + -18y + 9y2 = (5 + -6y) Solving 8 + -18y + 9y2 = 5 + -6y Solving for variable 'y'. Reorder the terms: 8 + -5 + -18y + 6y + 9y2 = 5 + -6y + -5 + 6y Combine like terms: 8 + -5 = 3 3 + -18y + 6y + 9y2 = 5 + -6y + -5 + 6y Combine like terms: -18y + 6y = -12y 3 + -12y + 9y2 = 5 + -6y + -5 + 6y Reorder the terms: 3 + -12y + 9y2 = 5 + -5 + -6y + 6y Combine like terms: 5 + -5 = 0 3 + -12y + 9y2 = 0 + -6y + 6y 3 + -12y + 9y2 = -6y + 6y Combine like terms: -6y + 6y = 0 3 + -12y + 9y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -4y + 3y2) = 0 Factor a trinomial. 3((1 + -3y)(1 + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 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 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Subproblem 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 = {0.3333333333, 1}
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