2u^3(5u+2)(u+3)=0

Solution for 2u^3(5u+2)(u+3)=0 equation:

Simplifying
2u3(5u + 2)(u + 3) = 0

Reorder the terms:
2u3(2 + 5u)(u + 3) = 0

Reorder the terms:
2u3(2 + 5u)(3 + u) = 0

Multiply (2 + 5u) * (3 + u)
2u3(2(3 + u) + 5u * (3 + u)) = 0
2u3((3 * 2 + u * 2) + 5u * (3 + u)) = 0
2u3((6 + 2u) + 5u * (3 + u)) = 0
2u3(6 + 2u + (3 * 5u + u * 5u)) = 0
2u3(6 + 2u + (15u + 5u2)) = 0

Combine like terms: 2u + 15u = 17u
2u3(6 + 17u + 5u2) = 0
(6 * 2u3 + 17u * 2u3 + 5u2 * 2u3) = 0
(12u3 + 34u4 + 10u5) = 0

Solving
12u3 + 34u4 + 10u5 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u3'.
2u3(6 + 17u + 5u2) = 0

Factor a trinomial.
2u3((3 + u)(2 + 5u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve:

Simplifying
u3 = 0

Solving
u3 = 0

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

Simplifying
u3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Subproblem 3
Set the factor '(2 + 5u)' equal to zero and attempt to solve:

Simplifying
2 + 5u = 0

Solving
2 + 5u = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5u = 0 + -2
5u = 0 + -2

Combine like terms: 0 + -2 = -2
5u = -2

Divide each side by '5'.
u = -0.4

Simplifying
u = -0.4
Solution
u = {-3, -0.4}