2u(u-3)(u+1)=0

Solution for 2u(u-3)(u+1)=0 equation:

Simplifying
2u(u + -3)(u + 1) = 0

Reorder the terms:
2u(-3 + u)(u + 1) = 0

Reorder the terms:
2u(-3 + u)(1 + u) = 0

Multiply (-3 + u) * (1 + u)
2u(-3(1 + u) + u(1 + u)) = 0
2u((1 * -3 + u * -3) + u(1 + u)) = 0
2u((-3 + -3u) + u(1 + u)) = 0
2u(-3 + -3u + (1 * u + u * u)) = 0
2u(-3 + -3u + (1u + u2)) = 0

Combine like terms: -3u + 1u = -2u
2u(-3 + -2u + u2) = 0
(-3 * 2u + -2u * 2u + u2 * 2u) = 0
(-6u + -4u2 + 2u3) = 0

Solving
-6u + -4u2 + 2u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u'.
2u(-3 + -2u + u2) = 0

Factor a trinomial.
2u((-1 + -1u)(3 + -1u)) = 0

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

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(-1 + -1u)' equal to zero and attempt to solve:

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1u = 0 + 1
-1u = 0 + 1

Combine like terms: 0 + 1 = 1
-1u = 1

Divide each side by '-1'.
u = -1

Simplifying
u = -1
Subproblem 3
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 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 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {0, -1, 3}