7(4-2u)6u=3

Solution for 7(4-2u)6u=3 equation:

Simplifying
7(4 + -2u) * 6u = 3

Reorder the terms for easier multiplication:
7 * 6u(4 + -2u) = 3

Multiply 7 * 6
42u(4 + -2u) = 3
(4 * 42u + -2u * 42u) = 3
(168u + -84u2) = 3

Solving
168u + -84u2 = 3

Solving for variable 'u'.

Reorder the terms:
-3 + 168u + -84u2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 168u + -84u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 56u + -28u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 56u + -28u2)' equal to zero and attempt to solve:

Simplifying
-1 + 56u + -28u2 = 0

Solving
-1 + 56u + -28u2 = 0

Begin completing the square.  Divide all terms by
-28 the coefficient of the squared term: 

Divide each side by '-28'.
0.03571428571 + -2u + u2 = 0

Move the constant term to the right:

Add '-0.03571428571' to each side of the equation.
0.03571428571 + -2u + -0.03571428571 + u2 = 0 + -0.03571428571

Reorder the terms:
0.03571428571 + -0.03571428571 + -2u + u2 = 0 + -0.03571428571

Combine like terms: 0.03571428571 + -0.03571428571 = 0.00000000000
0.00000000000 + -2u + u2 = 0 + -0.03571428571
-2u + u2 = 0 + -0.03571428571

Combine like terms: 0 + -0.03571428571 = -0.03571428571
-2u + u2 = -0.03571428571

The u term is -2u.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2u + 1 + u2 = -0.03571428571 + 1

Reorder the terms:
1 + -2u + u2 = -0.03571428571 + 1

Combine like terms: -0.03571428571 + 1 = 0.96428571429
1 + -2u + u2 = 0.96428571429

Factor a perfect square on the left side:
(u + -1)(u + -1) = 0.96428571429

Calculate the square root of the right side: 0.981980506

Break this problem into two subproblems by setting 
(u + -1) equal to 0.981980506 and -0.981980506.

Subproblem 1
u + -1 = 0.981980506

Simplifying
u + -1 = 0.981980506

Reorder the terms:
-1 + u = 0.981980506

Solving
-1 + u = 0.981980506

Solving for variable 'u'.

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

Add '1' to each side of the equation.
-1 + 1 + u = 0.981980506 + 1

Combine like terms: -1 + 1 = 0
0 + u = 0.981980506 + 1
u = 0.981980506 + 1

Combine like terms: 0.981980506 + 1 = 1.981980506
u = 1.981980506

Simplifying
u = 1.981980506

Subproblem 2
u + -1 = -0.981980506

Simplifying
u + -1 = -0.981980506

Reorder the terms:
-1 + u = -0.981980506

Solving
-1 + u = -0.981980506

Solving for variable 'u'.

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

Add '1' to each side of the equation.
-1 + 1 + u = -0.981980506 + 1

Combine like terms: -1 + 1 = 0
0 + u = -0.981980506 + 1
u = -0.981980506 + 1

Combine like terms: -0.981980506 + 1 = 0.018019494
u = 0.018019494

Simplifying
u = 0.018019494

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.981980506, 0.018019494}
Solution
u = {1.981980506, 0.018019494}