-t^2(4t-8)=0

Solution for -t^2(4t-8)=0 equation:

Simplifying
-1t2(4t + -8) = 0

Reorder the terms:
-1t2(-8 + 4t) = 0
(-8 * -1t2 + 4t * -1t2) = 0
(8t2 + -4t3) = 0

Solving
8t2 + -4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t2'.
4t2(2 + -1t) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0, 2}