4(-4t^2+24t-27)=0

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

Simplifying
4(-4t2 + 24t + -27) = 0

Reorder the terms:
4(-27 + 24t + -4t2) = 0
(-27 * 4 + 24t * 4 + -4t2 * 4) = 0
(-108 + 96t + -16t2) = 0

Solving
-108 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + 24t + -4t2) = 0

Factor a trinomial.
4((-9 + 2t)(3 + -2t)) = 0

Ignore the factor 4.
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}