5(u+6)(u+6)=60

Solution for 5(u+6)(u+6)=60 equation:

Simplifying
5(u + 6)(u + 6) = 60

Reorder the terms:
5(6 + u)(u + 6) = 60

Reorder the terms:
5(6 + u)(6 + u) = 60

Multiply (6 + u) * (6 + u)
5(6(6 + u) + u(6 + u)) = 60
5((6 * 6 + u * 6) + u(6 + u)) = 60
5((36 + 6u) + u(6 + u)) = 60
5(36 + 6u + (6 * u + u * u)) = 60
5(36 + 6u + (6u + u2)) = 60

Combine like terms: 6u + 6u = 12u
5(36 + 12u + u2) = 60
(36 * 5 + 12u * 5 + u2 * 5) = 60
(180 + 60u + 5u2) = 60

Solving
180 + 60u + 5u2 = 60

Solving for variable 'u'.

Reorder the terms:
180 + -60 + 60u + 5u2 = 60 + -60

Combine like terms: 180 + -60 = 120
120 + 60u + 5u2 = 60 + -60

Combine like terms: 60 + -60 = 0
120 + 60u + 5u2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + 12u + u2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(24 + 12u + u2)' equal to zero and attempt to solve:

Simplifying
24 + 12u + u2 = 0

Solving
24 + 12u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 12u + -24 + u2 = 0 + -24

Reorder the terms:
24 + -24 + 12u + u2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 12u + u2 = 0 + -24
12u + u2 = 0 + -24

Combine like terms: 0 + -24 = -24
12u + u2 = -24

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 = -24 + 36

Reorder the terms:
36 + 12u + u2 = -24 + 36

Combine like terms: -24 + 36 = 12
36 + 12u + u2 = 12

Factor a perfect square on the left side:
(u + 6)(u + 6) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(u + 6) equal to 3.464101615 and -3.464101615.

Subproblem 1
u + 6 = 3.464101615

Simplifying
u + 6 = 3.464101615

Reorder the terms:
6 + u = 3.464101615

Solving
6 + u = 3.464101615

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 = 3.464101615 + -6

Combine like terms: 6 + -6 = 0
0 + u = 3.464101615 + -6
u = 3.464101615 + -6

Combine like terms: 3.464101615 + -6 = -2.535898385
u = -2.535898385

Simplifying
u = -2.535898385

Subproblem 2
u + 6 = -3.464101615

Simplifying
u + 6 = -3.464101615

Reorder the terms:
6 + u = -3.464101615

Solving
6 + u = -3.464101615

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 = -3.464101615 + -6

Combine like terms: 6 + -6 = 0
0 + u = -3.464101615 + -6
u = -3.464101615 + -6

Combine like terms: -3.464101615 + -6 = -9.464101615
u = -9.464101615

Simplifying
u = -9.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-2.535898385, -9.464101615}
Solution
u = {-2.535898385, -9.464101615}