t^2=t+72

Solution for t^2=t+72 equation:

Simplifying
t2 = t + 72

Reorder the terms:
t2 = 72 + t

Solving
t2 = 72 + t

Solving for variable 't'.

Reorder the terms:
-72 + -1t + t2 = 72 + t + -72 + -1t

Reorder the terms:
-72 + -1t + t2 = 72 + -72 + t + -1t

Combine like terms: 72 + -72 = 0
-72 + -1t + t2 = 0 + t + -1t
-72 + -1t + t2 = t + -1t

Combine like terms: t + -1t = 0
-72 + -1t + t2 = 0

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

Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

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

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

Divide each side by '-1'.
t = -8

Simplifying
t = -8
Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

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

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

Divide each side by '-1'.
t = 9

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