480-480(u-8)=3u(u-8)

Solution for 480-480(u-8)=3u(u-8) equation:

Simplifying
480 + -480(u + -8) = 3u(u + -8)

Reorder the terms:
480 + -480(-8 + u) = 3u(u + -8)
480 + (-8 * -480 + u * -480) = 3u(u + -8)
480 + (3840 + -480u) = 3u(u + -8)

Combine like terms: 480 + 3840 = 4320
4320 + -480u = 3u(u + -8)

Reorder the terms:
4320 + -480u = 3u(-8 + u)
4320 + -480u = (-8 * 3u + u * 3u)
4320 + -480u = (-24u + 3u2)

Solving
4320 + -480u = -24u + 3u2

Solving for variable 'u'.

Combine like terms: -480u + 24u = -456u
4320 + -456u + -3u2 = -24u + 3u2 + 24u + -3u2

Reorder the terms:
4320 + -456u + -3u2 = -24u + 24u + 3u2 + -3u2

Combine like terms: -24u + 24u = 0
4320 + -456u + -3u2 = 0 + 3u2 + -3u2
4320 + -456u + -3u2 = 3u2 + -3u2

Combine like terms: 3u2 + -3u2 = 0
4320 + -456u + -3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1440 + -152u + -1u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1440 + -152u + -1u2)' equal to zero and attempt to solve:

Simplifying
1440 + -152u + -1u2 = 0

Solving
1440 + -152u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1440 + 152u + u2 = 0

Move the constant term to the right:

Add '1440' to each side of the equation.
-1440 + 152u + 1440 + u2 = 0 + 1440

Reorder the terms:
-1440 + 1440 + 152u + u2 = 0 + 1440

Combine like terms: -1440 + 1440 = 0
0 + 152u + u2 = 0 + 1440
152u + u2 = 0 + 1440

Combine like terms: 0 + 1440 = 1440
152u + u2 = 1440

The u term is 152u.  Take half its coefficient (76).
Square it (5776) and add it to both sides.

Add '5776' to each side of the equation.
152u + 5776 + u2 = 1440 + 5776

Reorder the terms:
5776 + 152u + u2 = 1440 + 5776

Combine like terms: 1440 + 5776 = 7216
5776 + 152u + u2 = 7216

Factor a perfect square on the left side:
(u + 76)(u + 76) = 7216

Calculate the square root of the right side: 84.947042326

Break this problem into two subproblems by setting 
(u + 76) equal to 84.947042326 and -84.947042326.

Subproblem 1
u + 76 = 84.947042326

Simplifying
u + 76 = 84.947042326

Reorder the terms:
76 + u = 84.947042326

Solving
76 + u = 84.947042326

Solving for variable 'u'.

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

Add '-76' to each side of the equation.
76 + -76 + u = 84.947042326 + -76

Combine like terms: 76 + -76 = 0
0 + u = 84.947042326 + -76
u = 84.947042326 + -76

Combine like terms: 84.947042326 + -76 = 8.947042326
u = 8.947042326

Simplifying
u = 8.947042326

Subproblem 2
u + 76 = -84.947042326

Simplifying
u + 76 = -84.947042326

Reorder the terms:
76 + u = -84.947042326

Solving
76 + u = -84.947042326

Solving for variable 'u'.

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

Add '-76' to each side of the equation.
76 + -76 + u = -84.947042326 + -76

Combine like terms: 76 + -76 = 0
0 + u = -84.947042326 + -76
u = -84.947042326 + -76

Combine like terms: -84.947042326 + -76 = -160.947042326
u = -160.947042326

Simplifying
u = -160.947042326

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {8.947042326, -160.947042326}
Solution
u = {8.947042326, -160.947042326}