7t^3+16t^2+4t=0

Solution for 7t^3+16t^2+4t=0 equation:

Simplifying
7t3 + 16t2 + 4t = 0

Reorder the terms:
4t + 16t2 + 7t3 = 0

Solving
4t + 16t2 + 7t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(4 + 16t + 7t2) = 0

Factor a trinomial.
t((2 + t)(2 + 7t)) = 0

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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Subproblem 3
Set the factor '(2 + 7t)' equal to zero and attempt to solve:

Simplifying
2 + 7t = 0

Solving
2 + 7t = 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 + 7t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7t = 0 + -2
7t = 0 + -2

Combine like terms: 0 + -2 = -2
7t = -2

Divide each side by '7'.
t = -0.2857142857

Simplifying
t = -0.2857142857
Solution
t = {0, -2, -0.2857142857}