y^2+6y+32=-5y+2

Solution for y^2+6y+32=-5y+2 equation:

Simplifying
y2 + 6y + 32 = -5y + 2

Reorder the terms:
32 + 6y + y2 = -5y + 2

Reorder the terms:
32 + 6y + y2 = 2 + -5y

Solving
32 + 6y + y2 = 2 + -5y

Solving for variable 'y'.

Reorder the terms:
32 + -2 + 6y + 5y + y2 = 2 + -5y + -2 + 5y

Combine like terms: 32 + -2 = 30
30 + 6y + 5y + y2 = 2 + -5y + -2 + 5y

Combine like terms: 6y + 5y = 11y
30 + 11y + y2 = 2 + -5y + -2 + 5y

Reorder the terms:
30 + 11y + y2 = 2 + -2 + -5y + 5y

Combine like terms: 2 + -2 = 0
30 + 11y + y2 = 0 + -5y + 5y
30 + 11y + y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
30 + 11y + y2 = 0

Factor a trinomial.
(6 + y)(5 + y) = 0

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5
Solution
y = {-6, -5}