-4(u+7)2u-46=

Solution for -4(u+7)2u-46= equation:

Simplifying
-4(u + 7) * 2u + -46 = 0

Reorder the terms:
-4(7 + u) * 2u + -46 = 0

Reorder the terms for easier multiplication:
-4 * 2u(7 + u) + -46 = 0

Multiply -4 * 2
-8u(7 + u) + -46 = 0
(7 * -8u + u * -8u) + -46 = 0
(-56u + -8u2) + -46 = 0

Reorder the terms:
-46 + -56u + -8u2 = 0

Solving
-46 + -56u + -8u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(23 + 28u + 4u2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(23 + 28u + 4u2)' equal to zero and attempt to solve:

Simplifying
23 + 28u + 4u2 = 0

Solving
23 + 28u + 4u2 = 0

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

Divide each side by '4'.
5.75 + 7u + u2 = 0

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + 7u + -5.75 + u2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + 7u + u2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + 7u + u2 = 0 + -5.75
7u + u2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
7u + u2 = -5.75

The u term is 7u.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7u + 12.25 + u2 = -5.75 + 12.25

Reorder the terms:
12.25 + 7u + u2 = -5.75 + 12.25

Combine like terms: -5.75 + 12.25 = 6.5
12.25 + 7u + u2 = 6.5

Factor a perfect square on the left side:
(u + 3.5)(u + 3.5) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(u + 3.5) equal to 2.549509757 and -2.549509757.

Subproblem 1
u + 3.5 = 2.549509757

Simplifying
u + 3.5 = 2.549509757

Reorder the terms:
3.5 + u = 2.549509757

Solving
3.5 + u = 2.549509757

Solving for variable 'u'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + u = 2.549509757 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + u = 2.549509757 + -3.5
u = 2.549509757 + -3.5

Combine like terms: 2.549509757 + -3.5 = -0.950490243
u = -0.950490243

Simplifying
u = -0.950490243

Subproblem 2
u + 3.5 = -2.549509757

Simplifying
u + 3.5 = -2.549509757

Reorder the terms:
3.5 + u = -2.549509757

Solving
3.5 + u = -2.549509757

Solving for variable 'u'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + u = -2.549509757 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + u = -2.549509757 + -3.5
u = -2.549509757 + -3.5

Combine like terms: -2.549509757 + -3.5 = -6.049509757
u = -6.049509757

Simplifying
u = -6.049509757

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.950490243, -6.049509757}
Solution
u = {-0.950490243, -6.049509757}