(7x-2)(6x+4)=x

Solution for (7x-2)(6x+4)=x equation:

Simplifying
(7x + -2)(6x + 4) = x

Reorder the terms:
(-2 + 7x)(6x + 4) = x

Reorder the terms:
(-2 + 7x)(4 + 6x) = x

Multiply (-2 + 7x) * (4 + 6x)
(-2(4 + 6x) + 7x * (4 + 6x)) = x
((4 * -2 + 6x * -2) + 7x * (4 + 6x)) = x
((-8 + -12x) + 7x * (4 + 6x)) = x
(-8 + -12x + (4 * 7x + 6x * 7x)) = x
(-8 + -12x + (28x + 42x2)) = x

Combine like terms: -12x + 28x = 16x
(-8 + 16x + 42x2) = x

Solving
-8 + 16x + 42x2 = x

Solving for variable 'x'.

Reorder the terms:
-8 + 16x + -1x + 42x2 = x + -1x

Combine like terms: 16x + -1x = 15x
-8 + 15x + 42x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 15x + 42x2 = 0

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

Divide each side by '42'.
-0.1904761905 + 0.3571428571x + x2 = 0

Move the constant term to the right:

Add '0.1904761905' to each side of the equation.
-0.1904761905 + 0.3571428571x + 0.1904761905 + x2 = 0 + 0.1904761905

Reorder the terms:
-0.1904761905 + 0.1904761905 + 0.3571428571x + x2 = 0 + 0.1904761905

Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000
0.0000000000 + 0.3571428571x + x2 = 0 + 0.1904761905
0.3571428571x + x2 = 0 + 0.1904761905

Combine like terms: 0 + 0.1904761905 = 0.1904761905
0.3571428571x + x2 = 0.1904761905

The x term is 0.3571428571x.  Take half its coefficient (0.1785714286).
Square it (0.03188775511) and add it to both sides.

Add '0.03188775511' to each side of the equation.
0.3571428571x + 0.03188775511 + x2 = 0.1904761905 + 0.03188775511

Reorder the terms:
0.03188775511 + 0.3571428571x + x2 = 0.1904761905 + 0.03188775511

Combine like terms: 0.1904761905 + 0.03188775511 = 0.22236394561
0.03188775511 + 0.3571428571x + x2 = 0.22236394561

Factor a perfect square on the left side:
(x + 0.1785714286)(x + 0.1785714286) = 0.22236394561

Calculate the square root of the right side: 0.471554817

Break this problem into two subproblems by setting 
(x + 0.1785714286) equal to 0.471554817 and -0.471554817.

Subproblem 1
x + 0.1785714286 = 0.471554817

Simplifying
x + 0.1785714286 = 0.471554817

Reorder the terms:
0.1785714286 + x = 0.471554817

Solving
0.1785714286 + x = 0.471554817

Solving for variable 'x'.

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

Add '-0.1785714286' to each side of the equation.
0.1785714286 + -0.1785714286 + x = 0.471554817 + -0.1785714286

Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000
0.0000000000 + x = 0.471554817 + -0.1785714286
x = 0.471554817 + -0.1785714286

Combine like terms: 0.471554817 + -0.1785714286 = 0.2929833884
x = 0.2929833884

Simplifying
x = 0.2929833884

Subproblem 2
x + 0.1785714286 = -0.471554817

Simplifying
x + 0.1785714286 = -0.471554817

Reorder the terms:
0.1785714286 + x = -0.471554817

Solving
0.1785714286 + x = -0.471554817

Solving for variable 'x'.

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

Add '-0.1785714286' to each side of the equation.
0.1785714286 + -0.1785714286 + x = -0.471554817 + -0.1785714286

Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000
0.0000000000 + x = -0.471554817 + -0.1785714286
x = -0.471554817 + -0.1785714286

Combine like terms: -0.471554817 + -0.1785714286 = -0.6501262456
x = -0.6501262456

Simplifying
x = -0.6501262456

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2929833884, -0.6501262456}