3u(u-2)=10

Solution for 3u(u-2)=10 equation:

Simplifying
3u(u + -2) = 10

Reorder the terms:
3u(-2 + u) = 10
(-2 * 3u + u * 3u) = 10
(-6u + 3u2) = 10

Solving
-6u + 3u2 = 10

Solving for variable 'u'.

Reorder the terms:
-10 + -6u + 3u2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -6u + 3u2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.333333333 + -2u + u2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -2u + 3.333333333 + u2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -2u + u2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -2u + u2 = 0 + 3.333333333
-2u + u2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-2u + u2 = 3.333333333

The u term is -2u.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2u + 1 + u2 = 3.333333333 + 1

Reorder the terms:
1 + -2u + u2 = 3.333333333 + 1

Combine like terms: 3.333333333 + 1 = 4.333333333
1 + -2u + u2 = 4.333333333

Factor a perfect square on the left side:
(u + -1)(u + -1) = 4.333333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(u + -1) equal to 2.081665999 and -2.081665999.

Subproblem 1
u + -1 = 2.081665999

Simplifying
u + -1 = 2.081665999

Reorder the terms:
-1 + u = 2.081665999

Solving
-1 + u = 2.081665999

Solving for variable 'u'.

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 = 2.081665999 + 1

Combine like terms: -1 + 1 = 0
0 + u = 2.081665999 + 1
u = 2.081665999 + 1

Combine like terms: 2.081665999 + 1 = 3.081665999
u = 3.081665999

Simplifying
u = 3.081665999

Subproblem 2
u + -1 = -2.081665999

Simplifying
u + -1 = -2.081665999

Reorder the terms:
-1 + u = -2.081665999

Solving
-1 + u = -2.081665999

Solving for variable 'u'.

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 = -2.081665999 + 1

Combine like terms: -1 + 1 = 0
0 + u = -2.081665999 + 1
u = -2.081665999 + 1

Combine like terms: -2.081665999 + 1 = -1.081665999
u = -1.081665999

Simplifying
u = -1.081665999

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.081665999, -1.081665999}