13=y^2-3y-5

Solution for 13=y^2-3y-5 equation:

Simplifying
13 = y2 + -3y + -5

Reorder the terms:
13 = -5 + -3y + y2

Solving
13 = -5 + -3y + y2

Solving for variable 'y'.

Combine like terms: 13 + 5 = 18
18 + 3y + -1y2 = -5 + -3y + y2 + 5 + 3y + -1y2

Reorder the terms:
18 + 3y + -1y2 = -5 + 5 + -3y + 3y + y2 + -1y2

Combine like terms: -5 + 5 = 0
18 + 3y + -1y2 = 0 + -3y + 3y + y2 + -1y2
18 + 3y + -1y2 = -3y + 3y + y2 + -1y2

Combine like terms: -3y + 3y = 0
18 + 3y + -1y2 = 0 + y2 + -1y2
18 + 3y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
18 + 3y + -1y2 = 0

Factor a trinomial.
(6 + -1y)(3 + y) = 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 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

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