y^2=y+6

Solution for y^2=y+6 equation:

Simplifying
y2 = y + 6

Reorder the terms:
y2 = 6 + y

Solving
y2 = 6 + y

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(-2 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
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 = {-2, 3}