4u(u+4)=2u+28

Solution for 4u(u+4)=2u+28 equation:

Simplifying
4u(u + 4) = 2u + 28

Reorder the terms:
4u(4 + u) = 2u + 28
(4 * 4u + u * 4u) = 2u + 28
(16u + 4u2) = 2u + 28

Reorder the terms:
16u + 4u2 = 28 + 2u

Solving
16u + 4u2 = 28 + 2u

Solving for variable 'u'.

Reorder the terms:
-28 + 16u + -2u + 4u2 = 28 + 2u + -28 + -2u

Combine like terms: 16u + -2u = 14u
-28 + 14u + 4u2 = 28 + 2u + -28 + -2u

Reorder the terms:
-28 + 14u + 4u2 = 28 + -28 + 2u + -2u

Combine like terms: 28 + -28 = 0
-28 + 14u + 4u2 = 0 + 2u + -2u
-28 + 14u + 4u2 = 2u + -2u

Combine like terms: 2u + -2u = 0
-28 + 14u + 4u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 7u + 2u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 7u + 2u2)' equal to zero and attempt to solve:

Simplifying
-14 + 7u + 2u2 = 0

Solving
-14 + 7u + 2u2 = 0

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

Divide each side by '2'.
-7 + 3.5u + u2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3.5u + 7 + u2 = 0 + 7

Reorder the terms:
-7 + 7 + 3.5u + u2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3.5u + u2 = 0 + 7
3.5u + u2 = 0 + 7

Combine like terms: 0 + 7 = 7
3.5u + u2 = 7

The u term is 3.5u.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5u + 3.0625 + u2 = 7 + 3.0625

Reorder the terms:
3.0625 + 3.5u + u2 = 7 + 3.0625

Combine like terms: 7 + 3.0625 = 10.0625
3.0625 + 3.5u + u2 = 10.0625

Factor a perfect square on the left side:
(u + 1.75)(u + 1.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(u + 1.75) equal to 3.172144385 and -3.172144385.

Subproblem 1
u + 1.75 = 3.172144385

Simplifying
u + 1.75 = 3.172144385

Reorder the terms:
1.75 + u = 3.172144385

Solving
1.75 + u = 3.172144385

Solving for variable 'u'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + u = 3.172144385 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + u = 3.172144385 + -1.75
u = 3.172144385 + -1.75

Combine like terms: 3.172144385 + -1.75 = 1.422144385
u = 1.422144385

Simplifying
u = 1.422144385

Subproblem 2
u + 1.75 = -3.172144385

Simplifying
u + 1.75 = -3.172144385

Reorder the terms:
1.75 + u = -3.172144385

Solving
1.75 + u = -3.172144385

Solving for variable 'u'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + u = -3.172144385 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + u = -3.172144385 + -1.75
u = -3.172144385 + -1.75

Combine like terms: -3.172144385 + -1.75 = -4.922144385
u = -4.922144385

Simplifying
u = -4.922144385

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.422144385, -4.922144385}
Solution
u = {1.422144385, -4.922144385}