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

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

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

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

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

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

Solving for variable 'y'.

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

Combine like terms: 11 + 1 = 12
12 + -2y + -5y + y2 = -1 + 5y + 1 + -5y

Combine like terms: -2y + -5y = -7y
12 + -7y + y2 = -1 + 5y + 1 + -5y

Reorder the terms:
12 + -7y + y2 = -1 + 1 + 5y + -5y

Combine like terms: -1 + 1 = 0
12 + -7y + y2 = 0 + 5y + -5y
12 + -7y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
12 + -7y + y2 = 0

Factor a trinomial.
(3 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {3, 4}