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

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


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

Reorder the terms:
-4u(2 + u) = 7u + -2
(2 * -4u + u * -4u) = 7u + -2
(-8u + -4u2) = 7u + -2

Reorder the terms:
-8u + -4u2 = -2 + 7u

Solving
-8u + -4u2 = -2 + 7u

Solving for variable 'u'.

Reorder the terms:
2 + -8u + -7u + -4u2 = -2 + 7u + 2 + -7u

Combine like terms: -8u + -7u = -15u
2 + -15u + -4u2 = -2 + 7u + 2 + -7u

Reorder the terms:
2 + -15u + -4u2 = -2 + 2 + 7u + -7u

Combine like terms: -2 + 2 = 0
2 + -15u + -4u2 = 0 + 7u + -7u
2 + -15u + -4u2 = 7u + -7u

Combine like terms: 7u + -7u = 0
2 + -15u + -4u2 = 0

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

Divide each side by '-4'.
-0.5 + 3.75u + u2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3.75u + 0.5 + u2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3.75u + u2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3.75u + u2 = 0 + 0.5
3.75u + u2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3.75u + u2 = 0.5

The u term is 3.75u.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75u + 3.515625 + u2 = 0.5 + 3.515625

Reorder the terms:
3.515625 + 3.75u + u2 = 0.5 + 3.515625

Combine like terms: 0.5 + 3.515625 = 4.015625
3.515625 + 3.75u + u2 = 4.015625

Factor a perfect square on the left side:
(u + 1.875)(u + 1.875) = 4.015625

Calculate the square root of the right side: 2.003902443

Break this problem into two subproblems by setting 
(u + 1.875) equal to 2.003902443 and -2.003902443.


Subproblem 1
u + 1.875 = 2.003902443

Simplifying
u + 1.875 = 2.003902443

Reorder the terms:
1.875 + u = 2.003902443

Solving
1.875 + u = 2.003902443

Solving for variable 'u'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + u = 2.003902443 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + u = 2.003902443 + -1.875
u = 2.003902443 + -1.875

Combine like terms: 2.003902443 + -1.875 = 0.128902443
u = 0.128902443

Simplifying
u = 0.128902443


Subproblem 2
u + 1.875 = -2.003902443

Simplifying
u + 1.875 = -2.003902443

Reorder the terms:
1.875 + u = -2.003902443

Solving
1.875 + u = -2.003902443

Solving for variable 'u'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + u = -2.003902443 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + u = -2.003902443 + -1.875
u = -2.003902443 + -1.875

Combine like terms: -2.003902443 + -1.875 = -3.878902443
u = -3.878902443

Simplifying
u = -3.878902443


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.128902443, -3.878902443}

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