y^2-5y+11=2y+1

Solution for y^2-5y+11=2y+1 equation:

Simplifying
y2 + -5y + 11 = 2y + 1

Reorder the terms:
11 + -5y + y2 = 2y + 1

Reorder the terms:
11 + -5y + y2 = 1 + 2y

Solving
11 + -5y + y2 = 1 + 2y

Solving for variable 'y'.

Reorder the terms:
11 + -1 + -5y + -2y + y2 = 1 + 2y + -1 + -2y

Combine like terms: 11 + -1 = 10
10 + -5y + -2y + y2 = 1 + 2y + -1 + -2y

Combine like terms: -5y + -2y = -7y
10 + -7y + y2 = 1 + 2y + -1 + -2y

Reorder the terms:
10 + -7y + y2 = 1 + -1 + 2y + -2y

Combine like terms: 1 + -1 = 0
10 + -7y + y2 = 0 + 2y + -2y
10 + -7y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
10 + -7y + y2 = 0

Factor a trinomial.
(2 + -1y)(5 + -1y) = 0

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
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 = {2, 5}