4t^2+24t+27=0

Solution for 4t^2+24t+27=0 equation:

Simplifying
4t2 + 24t + 27 = 0

Reorder the terms:
27 + 24t + 4t2 = 0

Solving
27 + 24t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(9 + 2t)(3 + 2t) = 0

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

Simplifying
3 + 2t = 0

Solving
3 + 2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {-4.5, -1.5}