5t^2+39t+54=0

Solution for 5t^2+39t+54=0 equation:

Simplifying
5t2 + 39t + 54 = 0

Reorder the terms:
54 + 39t + 5t2 = 0

Solving
54 + 39t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + t)(9 + 5t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + 5t)' equal to zero and attempt to solve:

Simplifying
9 + 5t = 0

Solving
9 + 5t = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5t = 0 + -9
5t = 0 + -9

Combine like terms: 0 + -9 = -9
5t = -9

Divide each side by '5'.
t = -1.8

Simplifying
t = -1.8
Solution
t = {-6, -1.8}