T^2+14T=120

Solution for T^2+14T=120 equation:

Simplifying
T2 + 14T = 120

Reorder the terms:
14T + T2 = 120

Solving
14T + T2 = 120

Solving for variable 'T'.

Reorder the terms:
-120 + 14T + T2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 14T + T2 = 0

Factor a trinomial.
(-20 + -1T)(6 + -1T) = 0

Subproblem 1
Set the factor '(-20 + -1T)' equal to zero and attempt to solve:

Simplifying
-20 + -1T = 0

Solving
-20 + -1T = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1T = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1T = 0 + 20
-1T = 0 + 20

Combine like terms: 0 + 20 = 20
-1T = 20

Divide each side by '-1'.
T = -20

Simplifying
T = -20
Subproblem 2
Set the factor '(6 + -1T)' equal to zero and attempt to solve:

Simplifying
6 + -1T = 0

Solving
6 + -1T = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1T = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1T = 0 + -6
-1T = 0 + -6

Combine like terms: 0 + -6 = -6
-1T = -6

Divide each side by '-1'.
T = 6

Simplifying
T = 6
Solution
T = {-20, 6}