0=2t-120+t^2

Solution for 0=2t-120+t^2 equation:

Simplifying
0 = 2t + -120 + t2

Reorder the terms:
0 = -120 + 2t + t2

Solving
0 = -120 + 2t + t2

Solving for variable 't'.

Combine like terms: 0 + 120 = 120
120 + -2t + -1t2 = -120 + 2t + t2 + 120 + -2t + -1t2

Reorder the terms:
120 + -2t + -1t2 = -120 + 120 + 2t + -2t + t2 + -1t2

Combine like terms: -120 + 120 = 0
120 + -2t + -1t2 = 0 + 2t + -2t + t2 + -1t2
120 + -2t + -1t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
120 + -2t + -1t2 = 0 + t2 + -1t2
120 + -2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
120 + -2t + -1t2 = 0

Factor a trinomial.
(10 + -1t)(12 + t) = 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 '(12 + t)' equal to zero and attempt to solve:

Simplifying
12 + t = 0

Solving
12 + t = 0

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

Add '-12' to each side of the equation.
12 + -12 + t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + t = 0 + -12
t = 0 + -12

Combine like terms: 0 + -12 = -12
t = -12

Simplifying
t = -12
Solution
t = {10, -12}