-2u(u-5)(u+1)=0

Solution for -2u(u-5)(u+1)=0 equation:

Simplifying
-2u(u + -5)(u + 1) = 0

Reorder the terms:
-2u(-5 + u)(u + 1) = 0

Reorder the terms:
-2u(-5 + u)(1 + u) = 0

Multiply (-5 + u) * (1 + u)
-2u(-5(1 + u) + u(1 + u)) = 0
-2u((1 * -5 + u * -5) + u(1 + u)) = 0
-2u((-5 + -5u) + u(1 + u)) = 0
-2u(-5 + -5u + (1 * u + u * u)) = 0
-2u(-5 + -5u + (1u + u2)) = 0

Combine like terms: -5u + 1u = -4u
-2u(-5 + -4u + u2) = 0
(-5 * -2u + -4u * -2u + u2 * -2u) = 0
(10u + 8u2 + -2u3) = 0

Solving
10u + 8u2 + -2u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u'.
2u(5 + 4u + -1u2) = 0

Factor a trinomial.
2u((5 + -1u)(1 + u)) = 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 '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Subproblem 3
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

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

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

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

Simplifying
u = -1
Solution
u = {0, 5, -1}