t^2=t+110

Solution for t^2=t+110 equation:

Simplifying
t2 = t + 110

Reorder the terms:
t2 = 110 + t

Solving
t2 = 110 + t

Solving for variable 't'.

Reorder the terms:
-110 + -1t + t2 = 110 + t + -110 + -1t

Reorder the terms:
-110 + -1t + t2 = 110 + -110 + t + -1t

Combine like terms: 110 + -110 = 0
-110 + -1t + t2 = 0 + t + -1t
-110 + -1t + t2 = t + -1t

Combine like terms: t + -1t = 0
-110 + -1t + t2 = 0

Factor a trinomial.
(-10 + -1t)(11 + -1t) = 0

Subproblem 1
Set the factor '(-10 + -1t)' equal to zero and attempt to solve:

Simplifying
-10 + -1t = 0

Solving
-10 + -1t = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1t = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1t = 0 + 10
-1t = 0 + 10

Combine like terms: 0 + 10 = 10
-1t = 10

Divide each side by '-1'.
t = -10

Simplifying
t = -10
Subproblem 2
Set the factor '(11 + -1t)' equal to zero and attempt to solve:

Simplifying
11 + -1t = 0

Solving
11 + -1t = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1t = 0 + -11
-1t = 0 + -11

Combine like terms: 0 + -11 = -11
-1t = -11

Divide each side by '-1'.
t = 11

Simplifying
t = 11
Solution
t = {-10, 11}