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Simplifying y2 + 3y + 8 = -2y + 4 Reorder the terms: 8 + 3y + y2 = -2y + 4 Reorder the terms: 8 + 3y + y2 = 4 + -2y Solving 8 + 3y + y2 = 4 + -2y Solving for variable 'y'. Reorder the terms: 8 + -4 + 3y + 2y + y2 = 4 + -2y + -4 + 2y Combine like terms: 8 + -4 = 4 4 + 3y + 2y + y2 = 4 + -2y + -4 + 2y Combine like terms: 3y + 2y = 5y 4 + 5y + y2 = 4 + -2y + -4 + 2y Reorder the terms: 4 + 5y + y2 = 4 + -4 + -2y + 2y Combine like terms: 4 + -4 = 0 4 + 5y + y2 = 0 + -2y + 2y 4 + 5y + y2 = -2y + 2y Combine like terms: -2y + 2y = 0 4 + 5y + y2 = 0 Factor a trinomial. (4 + y)(1 + y) = 0Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4Subproblem 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 = {-4, -1}
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