120=10t+5t^2

Solution for 120=10t+5t^2 equation:

Simplifying
120 = 10t + 5t2

Solving
120 = 10t + 5t2

Solving for variable 't'.

Reorder the terms:
120 + -10t + -5t2 = 10t + -10t + 5t2 + -5t2

Combine like terms: 10t + -10t = 0
120 + -10t + -5t2 = 0 + 5t2 + -5t2
120 + -10t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
120 + -10t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + -2t + -1t2) = 0

Factor a trinomial.
5((4 + -1t)(6 + t)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Solution
t = {4, -6}