-4(4t^2-12t-216)=0

Solution for -4(4t^2-12t-216)=0 equation:

Simplifying
-4(4t2 + -12t + -216) = 0

Reorder the terms:
-4(-216 + -12t + 4t2) = 0
(-216 * -4 + -12t * -4 + 4t2 * -4) = 0
(864 + 48t + -16t2) = 0

Solving
864 + 48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(54 + 3t + -1t2) = 0

Factor a trinomial.
16((9 + -1t)(6 + t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 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 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Subproblem 2
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
Solution
t = {9, -6}