t(t+2)=120

Solution for t(t+2)=120 equation:

Simplifying
t(t + 2) = 120

Reorder the terms:
t(2 + t) = 120
(2 * t + t * t) = 120
(2t + t2) = 120

Solving
2t + t2 = 120

Solving for variable 't'.

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

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

Factor a trinomial.
(-12 + -1t)(10 + -1t) = 0

Subproblem 1
Set the factor '(-12 + -1t)' equal to zero and attempt to solve:

Simplifying
-12 + -1t = 0

Solving
-12 + -1t = 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 + -1t = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1t = 0 + 12
-1t = 0 + 12

Combine like terms: 0 + 12 = 12
-1t = 12

Divide each side by '-1'.
t = -12

Simplifying
t = -12
Subproblem 2
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
Solution
t = {-12, 10}