27y+y^2=160

Solution for 27y+y^2=160 equation:

Simplifying
27y + y2 = 160

Solving
27y + y2 = 160

Solving for variable 'y'.

Reorder the terms:
-160 + 27y + y2 = 160 + -160

Combine like terms: 160 + -160 = 0
-160 + 27y + y2 = 0

Factor a trinomial.
(-32 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-32 + -1y)' equal to zero and attempt to solve:

Simplifying
-32 + -1y = 0

Solving
-32 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '32' to each side of the equation.
-32 + 32 + -1y = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1y = 0 + 32
-1y = 0 + 32

Combine like terms: 0 + 32 = 32
-1y = 32

Divide each side by '-1'.
y = -32

Simplifying
y = -32
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-32, 5}