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.
(3 + -2t)(9 + -2t) = 0

Subproblem 1
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
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 = {1.5, 4.5}