.5(4t^2-4)(3t)=0

Solution for .5(4t^2-4)(3t)=0 equation:

Simplifying
0.5(4t2 + -4)(3t) = 0

Reorder the terms:
0.5(-4 + 4t2)(3t) = 0

Remove parenthesis around (3t)
0.5(-4 + 4t2) * 3t = 0

Reorder the terms for easier multiplication:
0.5 * 3t(-4 + 4t2) = 0

Multiply 0.5 * 3
1.5t(-4 + 4t2) = 0
(-4 * 1.5t + 4t2 * 1.5t) = 0
(-6t + 6t3) = 0

Solving
-6t + 6t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t'.
6t(-1 + t2) = 0

Factor a difference between two squares.
6t((1 + t)(-1 + t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

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

Simplifying
-1 + t = 0

Solving
-1 + t = 0

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

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

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

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

Simplifying
t = 1
Solution
t = {0, -1, 1}