y^2+11y+11=5y+3

Solution for y^2+11y+11=5y+3 equation:

Simplifying
y2 + 11y + 11 = 5y + 3

Reorder the terms:
11 + 11y + y2 = 5y + 3

Reorder the terms:
11 + 11y + y2 = 3 + 5y

Solving
11 + 11y + y2 = 3 + 5y

Solving for variable 'y'.

Reorder the terms:
11 + -3 + 11y + -5y + y2 = 3 + 5y + -3 + -5y

Combine like terms: 11 + -3 = 8
8 + 11y + -5y + y2 = 3 + 5y + -3 + -5y

Combine like terms: 11y + -5y = 6y
8 + 6y + y2 = 3 + 5y + -3 + -5y

Reorder the terms:
8 + 6y + y2 = 3 + -3 + 5y + -5y

Combine like terms: 3 + -3 = 0
8 + 6y + y2 = 0 + 5y + -5y
8 + 6y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
8 + 6y + y2 = 0

Factor a trinomial.
(4 + y)(2 + y) = 0

Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

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

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

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

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

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Solution
y = {-4, -2}