2t^2+21t+54=0

Solution for 2t^2+21t+54=0 equation:

Simplifying
2t2 + 21t + 54 = 0

Reorder the terms:
54 + 21t + 2t2 = 0

Solving
54 + 21t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + t)(9 + 2t) = 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 + 2t)' equal to zero and attempt to solve:

Simplifying
9 + 2t = 0

Solving
9 + 2t = 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 + 2t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2t = 0 + -9
2t = 0 + -9

Combine like terms: 0 + -9 = -9
2t = -9

Divide each side by '2'.
t = -4.5

Simplifying
t = -4.5
Solution
t = {-6, -4.5}