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Simplifying (3y + 2)(1 + y) = 0 Reorder the terms: (2 + 3y)(1 + y) = 0 Multiply (2 + 3y) * (1 + y) (2(1 + y) + 3y * (1 + y)) = 0 ((1 * 2 + y * 2) + 3y * (1 + y)) = 0 ((2 + 2y) + 3y * (1 + y)) = 0 (2 + 2y + (1 * 3y + y * 3y)) = 0 (2 + 2y + (3y + 3y2)) = 0 Combine like terms: 2y + 3y = 5y (2 + 5y + 3y2) = 0 Solving 2 + 5y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (1 + y)(2 + 3y) = 0Subproblem 1
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 2
Set the factor '(2 + 3y)' equal to zero and attempt to solve: Simplifying 2 + 3y = 0 Solving 2 + 3y = 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 + 3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3y = 0 + -2 3y = 0 + -2 Combine like terms: 0 + -2 = -2 3y = -2 Divide each side by '3'. y = -0.6666666667 Simplifying y = -0.6666666667Solution
y = {-1, -0.6666666667}
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