0=y^2-5y-6

Solution for 0=y^2-5y-6 equation:

Simplifying
0 = y2 + -5y + -6

Reorder the terms:
0 = -6 + -5y + y2

Solving
0 = -6 + -5y + y2

Solving for variable 'y'.

Combine like terms: 0 + 6 = 6
6 + 5y + -1y2 = -6 + -5y + y2 + 6 + 5y + -1y2

Reorder the terms:
6 + 5y + -1y2 = -6 + 6 + -5y + 5y + y2 + -1y2

Combine like terms: -6 + 6 = 0
6 + 5y + -1y2 = 0 + -5y + 5y + y2 + -1y2
6 + 5y + -1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
6 + 5y + -1y2 = 0 + y2 + -1y2
6 + 5y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + 5y + -1y2 = 0

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

Add '-1' to each side of the equation.
1 + -1 + y = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {6, -1}