3u^2=18u-6

Solution for 3u^2=18u-6 equation:

Simplifying
3u2 = 18u + -6

Reorder the terms:
3u2 = -6 + 18u

Solving
3u2 = -6 + 18u

Solving for variable 'u'.

Reorder the terms:
6 + -18u + 3u2 = -6 + 18u + 6 + -18u

Reorder the terms:
6 + -18u + 3u2 = -6 + 6 + 18u + -18u

Combine like terms: -6 + 6 = 0
6 + -18u + 3u2 = 0 + 18u + -18u
6 + -18u + 3u2 = 18u + -18u

Combine like terms: 18u + -18u = 0
6 + -18u + 3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -6u + u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -6u + u2)' equal to zero and attempt to solve:

Simplifying
2 + -6u + u2 = 0

Solving
2 + -6u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6u + -2 + u2 = 0 + -2

Reorder the terms:
2 + -2 + -6u + u2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6u + u2 = 0 + -2
-6u + u2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6u + u2 = -2

The u term is -6u.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6u + 9 + u2 = -2 + 9

Reorder the terms:
9 + -6u + u2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6u + u2 = 7

Factor a perfect square on the left side:
(u + -3)(u + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(u + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1
u + -3 = 2.645751311

Simplifying
u + -3 = 2.645751311

Reorder the terms:
-3 + u = 2.645751311

Solving
-3 + u = 2.645751311

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + u = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + u = 2.645751311 + 3
u = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
u = 5.645751311

Simplifying
u = 5.645751311

Subproblem 2
u + -3 = -2.645751311

Simplifying
u + -3 = -2.645751311

Reorder the terms:
-3 + u = -2.645751311

Solving
-3 + u = -2.645751311

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + u = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + u = -2.645751311 + 3
u = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
u = 0.354248689

Simplifying
u = 0.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.645751311, 0.354248689}
Solution
u = {5.645751311, 0.354248689}