5t^2+4t-204=0

Solution for 5t^2+4t-204=0 equation:

Simplifying
5t2 + 4t + -204 = 0

Reorder the terms:
-204 + 4t + 5t2 = 0

Solving
-204 + 4t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-34 + -5t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-34 + -5t)' equal to zero and attempt to solve:

Simplifying
-34 + -5t = 0

Solving
-34 + -5t = 0

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

Add '34' to each side of the equation.
-34 + 34 + -5t = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -5t = 0 + 34
-5t = 0 + 34

Combine like terms: 0 + 34 = 34
-5t = 34

Divide each side by '-5'.
t = -6.8

Simplifying
t = -6.8
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 = {-6.8, 6}