7(x+1)(4x)=4

Solution for 7(x+1)(4x)=4 equation:

Simplifying
7(x + 1)(4x) = 4

Reorder the terms:
7(1 + x)(4x) = 4

Remove parenthesis around (4x)
7(1 + x) * 4x = 4

Reorder the terms for easier multiplication:
7 * 4x(1 + x) = 4

Multiply 7 * 4
28x(1 + x) = 4
(1 * 28x + x * 28x) = 4
(28x + 28x2) = 4

Solving
28x + 28x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 28x + 28x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 28x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 7x + 7x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 7x + 7x2)' equal to zero and attempt to solve:

Simplifying
-1 + 7x + 7x2 = 0

Solving
-1 + 7x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.1428571429
x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
x + x2 = 0.1428571429

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.1428571429 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.1428571429 + 0.25

Combine like terms: 0.1428571429 + 0.25 = 0.3928571429
1.25 + x2 = 0.3928571429

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.3928571429

Calculate the square root of the right side: 0.626783171

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.626783171 and -0.626783171.

Subproblem 1
x + 0.5 = 0.626783171

Simplifying
x + 0.5 = 0.626783171

Reorder the terms:
0.5 + x = 0.626783171

Solving
0.5 + x = 0.626783171

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.626783171 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.626783171 + -0.5
x = 0.626783171 + -0.5

Combine like terms: 0.626783171 + -0.5 = 0.126783171
x = 0.126783171

Simplifying
x = 0.126783171

Subproblem 2
x + 0.5 = -0.626783171

Simplifying
x + 0.5 = -0.626783171

Reorder the terms:
0.5 + x = -0.626783171

Solving
0.5 + x = -0.626783171

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.626783171 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.626783171 + -0.5
x = -0.626783171 + -0.5

Combine like terms: -0.626783171 + -0.5 = -1.126783171
x = -1.126783171

Simplifying
x = -1.126783171

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.126783171, -1.126783171}
Solution
x = {0.126783171, -1.126783171}