-3t^2+46t-120=0

Solution for -3t^2+46t-120=0 equation:

Simplifying
-3t2 + 46t + -120 = 0

Reorder the terms:
-120 + 46t + -3t2 = 0

Solving
-120 + 46t + -3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-12 + t)(10 + -3t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -3t)' equal to zero and attempt to solve:

Simplifying
10 + -3t = 0

Solving
10 + -3t = 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 + -3t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3t = 0 + -10
-3t = 0 + -10

Combine like terms: 0 + -10 = -10
-3t = -10

Divide each side by '-3'.
t = 3.333333333

Simplifying
t = 3.333333333
Solution
t = {12, 3.333333333}