y^2=y+72

Solution for y^2=y+72 equation:

Simplifying
y2 = y + 72

Reorder the terms:
y2 = 72 + y

Solving
y2 = 72 + y

Solving for variable 'y'.

Reorder the terms:
-72 + -1y + y2 = 72 + y + -72 + -1y

Reorder the terms:
-72 + -1y + y2 = 72 + -72 + y + -1y

Combine like terms: 72 + -72 = 0
-72 + -1y + y2 = 0 + y + -1y
-72 + -1y + y2 = y + -1y

Combine like terms: y + -1y = 0
-72 + -1y + y2 = 0

Factor a trinomial.
(-8 + -1y)(9 + -1y) = 0

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-8, 9}