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Simplifying y4 + y3 + 9y3 + 9y2 = 0 Reorder the terms: 9y2 + y3 + 9y3 + y4 = 0 Combine like terms: y3 + 9y3 = 10y3 9y2 + 10y3 + y4 = 0 Solving 9y2 + 10y3 + y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(9 + 10y + y2) = 0 Factor a trinomial. y2((9 + y)(1 + y)) = 0Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(9 + y)' equal to zero and attempt to solve: Simplifying 9 + y = 0 Solving 9 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + y = 0 + -9 y = 0 + -9 Combine like terms: 0 + -9 = -9 y = -9 Simplifying y = -9Subproblem 3
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 = {0, -9, -1}
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