4(4t^2+2t)=

Solution for 4(4t^2+2t)= equation:

Simplifying
4(4t2 + 2t) = 0

Reorder the terms:
4(2t + 4t2) = 0
(2t * 4 + 4t2 * 4) = 0
(8t + 16t2) = 0

Solving
8t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8t'.
8t(1 + 2t) = 0

Ignore the factor 8.
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 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

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

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

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {0, -0.5}