y^2+13y+10=5y-2

Solution for y^2+13y+10=5y-2 equation:

Simplifying
y2 + 13y + 10 = 5y + -2

Reorder the terms:
10 + 13y + y2 = 5y + -2

Reorder the terms:
10 + 13y + y2 = -2 + 5y

Solving
10 + 13y + y2 = -2 + 5y

Solving for variable 'y'.

Reorder the terms:
10 + 2 + 13y + -5y + y2 = -2 + 5y + 2 + -5y

Combine like terms: 10 + 2 = 12
12 + 13y + -5y + y2 = -2 + 5y + 2 + -5y

Combine like terms: 13y + -5y = 8y
12 + 8y + y2 = -2 + 5y + 2 + -5y

Reorder the terms:
12 + 8y + y2 = -2 + 2 + 5y + -5y

Combine like terms: -2 + 2 = 0
12 + 8y + y2 = 0 + 5y + -5y
12 + 8y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
12 + 8y + y2 = 0

Factor a trinomial.
(6 + y)(2 + 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 '(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 = {-6, -2}