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Simplifying y2 + 4y + 4 + -2y2 + -10y + -9 = 0 Reorder the terms: 4 + -9 + 4y + -10y + y2 + -2y2 = 0 Combine like terms: 4 + -9 = -5 -5 + 4y + -10y + y2 + -2y2 = 0 Combine like terms: 4y + -10y = -6y -5 + -6y + y2 + -2y2 = 0 Combine like terms: y2 + -2y2 = -1y2 -5 + -6y + -1y2 = 0 Solving -5 + -6y + -1y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 6y + y2) = 0 Factor a trinomial. -1((5 + y)(1 + y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Subproblem 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 = {-5, -1}
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