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