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

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

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

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

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

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

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

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

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u'.
2u(-2 + -1u + u2) = 0

Factor a trinomial.
2u((-1 + -1u)(2 + -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 '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 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 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {0, -1, 2}