7(u-6)(u-6)=56

Solution for 7(u-6)(u-6)=56 equation:

Simplifying
7(u + -6)(u + -6) = 56

Reorder the terms:
7(-6 + u)(u + -6) = 56

Reorder the terms:
7(-6 + u)(-6 + u) = 56

Multiply (-6 + u) * (-6 + u)
7(-6(-6 + u) + u(-6 + u)) = 56
7((-6 * -6 + u * -6) + u(-6 + u)) = 56
7((36 + -6u) + u(-6 + u)) = 56
7(36 + -6u + (-6 * u + u * u)) = 56
7(36 + -6u + (-6u + u2)) = 56

Combine like terms: -6u + -6u = -12u
7(36 + -12u + u2) = 56
(36 * 7 + -12u * 7 + u2 * 7) = 56
(252 + -84u + 7u2) = 56

Solving
252 + -84u + 7u2 = 56

Solving for variable 'u'.

Reorder the terms:
252 + -56 + -84u + 7u2 = 56 + -56

Combine like terms: 252 + -56 = 196
196 + -84u + 7u2 = 56 + -56

Combine like terms: 56 + -56 = 0
196 + -84u + 7u2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(28 + -12u + u2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(28 + -12u + u2)' equal to zero and attempt to solve:

Simplifying
28 + -12u + u2 = 0

Solving
28 + -12u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -12u + -28 + u2 = 0 + -28

Reorder the terms:
28 + -28 + -12u + u2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -12u + u2 = 0 + -28
-12u + u2 = 0 + -28

Combine like terms: 0 + -28 = -28
-12u + u2 = -28

The u term is -12u.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12u + 36 + u2 = -28 + 36

Reorder the terms:
36 + -12u + u2 = -28 + 36

Combine like terms: -28 + 36 = 8
36 + -12u + u2 = 8

Factor a perfect square on the left side:
(u + -6)(u + -6) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(u + -6) equal to 2.828427125 and -2.828427125.

Subproblem 1
u + -6 = 2.828427125

Simplifying
u + -6 = 2.828427125

Reorder the terms:
-6 + u = 2.828427125

Solving
-6 + u = 2.828427125

Solving for variable 'u'.

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

Add '6' to each side of the equation.
-6 + 6 + u = 2.828427125 + 6

Combine like terms: -6 + 6 = 0
0 + u = 2.828427125 + 6
u = 2.828427125 + 6

Combine like terms: 2.828427125 + 6 = 8.828427125
u = 8.828427125

Simplifying
u = 8.828427125

Subproblem 2
u + -6 = -2.828427125

Simplifying
u + -6 = -2.828427125

Reorder the terms:
-6 + u = -2.828427125

Solving
-6 + u = -2.828427125

Solving for variable 'u'.

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

Add '6' to each side of the equation.
-6 + 6 + u = -2.828427125 + 6

Combine like terms: -6 + 6 = 0
0 + u = -2.828427125 + 6
u = -2.828427125 + 6

Combine like terms: -2.828427125 + 6 = 3.171572875
u = 3.171572875

Simplifying
u = 3.171572875

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {8.828427125, 3.171572875}
Solution
u = {8.828427125, 3.171572875}