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Simplifying (3y + 1)(2 + -1y) = 0 Reorder the terms: (1 + 3y)(2 + -1y) = 0 Multiply (1 + 3y) * (2 + -1y) (1(2 + -1y) + 3y * (2 + -1y)) = 0 ((2 * 1 + -1y * 1) + 3y * (2 + -1y)) = 0 ((2 + -1y) + 3y * (2 + -1y)) = 0 (2 + -1y + (2 * 3y + -1y * 3y)) = 0 (2 + -1y + (6y + -3y2)) = 0 Combine like terms: -1y + 6y = 5y (2 + 5y + -3y2) = 0 Solving 2 + 5y + -3y2 = 0 Solving for variable 'y'. Factor a trinomial. (2 + -1y)(1 + 3y) = 0Subproblem 1
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Subproblem 2
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 = -0.3333333333Solution
y = {2, -0.3333333333}
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