50t^3+115t^2+60t=0

Solution for 50t^3+115t^2+60t=0 equation:

Simplifying
50t3 + 115t2 + 60t = 0

Reorder the terms:
60t + 115t2 + 50t3 = 0

Solving
60t + 115t2 + 50t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5t'.
5t(12 + 23t + 10t2) = 0

Factor a trinomial.
5t((3 + 2t)(4 + 5t)) = 0

Ignore the factor 5.
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 '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 3
Set the factor '(4 + 5t)' equal to zero and attempt to solve:

Simplifying
4 + 5t = 0

Solving
4 + 5t = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5t = 0 + -4
5t = 0 + -4

Combine like terms: 0 + -4 = -4
5t = -4

Divide each side by '5'.
t = -0.8

Simplifying
t = -0.8
Solution
t = {0, -1.5, -0.8}