y^2+8y-13=5y+5

Solution for y^2+8y-13=5y+5 equation:

Simplifying
y2 + 8y + -13 = 5y + 5

Reorder the terms:
-13 + 8y + y2 = 5y + 5

Reorder the terms:
-13 + 8y + y2 = 5 + 5y

Solving
-13 + 8y + y2 = 5 + 5y

Solving for variable 'y'.

Reorder the terms:
-13 + -5 + 8y + -5y + y2 = 5 + 5y + -5 + -5y

Combine like terms: -13 + -5 = -18
-18 + 8y + -5y + y2 = 5 + 5y + -5 + -5y

Combine like terms: 8y + -5y = 3y
-18 + 3y + y2 = 5 + 5y + -5 + -5y

Reorder the terms:
-18 + 3y + y2 = 5 + -5 + 5y + -5y

Combine like terms: 5 + -5 = 0
-18 + 3y + y2 = 0 + 5y + -5y
-18 + 3y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-18 + 3y + y2 = 0

Factor a trinomial.
(-6 + -1y)(3 + -1y) = 0

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

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 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 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
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
Solution
y = {-6, 3}