4t(2t^2+75t)=0

Solution for 4t(2t^2+75t)=0 equation:

Simplifying
4t(2t2 + 75t) = 0

Reorder the terms:
4t(75t + 2t2) = 0
(75t * 4t + 2t2 * 4t) = 0
(300t2 + 8t3) = 0

Solving
300t2 + 8t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t2'.
4t2(75 + 2t) = 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 '(75 + 2t)' equal to zero and attempt to solve:

Simplifying
75 + 2t = 0

Solving
75 + 2t = 0

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

Add '-75' to each side of the equation.
75 + -75 + 2t = 0 + -75

Combine like terms: 75 + -75 = 0
0 + 2t = 0 + -75
2t = 0 + -75

Combine like terms: 0 + -75 = -75
2t = -75

Divide each side by '2'.
t = -37.5

Simplifying
t = -37.5
Solution
t = {0, -37.5}