6u(2-u)=6

Solution for 6u(2-u)=6 equation:

Simplifying
6u(2 + -1u) = 6
(2 * 6u + -1u * 6u) = 6
(12u + -6u2) = 6

Solving
12u + -6u2 = 6

Solving for variable 'u'.

Reorder the terms:
-6 + 12u + -6u2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 12u + -6u2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2u + -1u2) = 0

Factor a trinomial.
6((-1 + u)(1 + -1u)) = 0

Ignore the factor 6.
Subproblem 1
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
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
Solution
u = {1, 1}