5u(-u)=4u

Solution for 5u(-u)=4u equation:

Simplifying
5u(-1u) = 4u

Remove parenthesis around (-1u)
5u * -1u = 4u

Reorder the terms for easier multiplication:
5 * -1u * u = 4u

Multiply 5 * -1
-5u * u = 4u

Multiply u * u
-5u2 = 4u

Solving
-5u2 = 4u

Solving for variable 'u'.

Reorder the terms:
-4u + -5u2 = 4u + -4u

Combine like terms: 4u + -4u = 0
-4u + -5u2 = 0

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

Ignore the factor -1.
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 '(4 + 5u)' equal to zero and attempt to solve:

Simplifying
4 + 5u = 0

Solving
4 + 5u = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5u = 0 + -4

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

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

Divide each side by '5'.
u = -0.8

Simplifying
u = -0.8
Solution
u = {0, -0.8}