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

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

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

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

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

Multiply (-4 + 7x) * (4 + 6x)
(-4(4 + 6x) + 7x * (4 + 6x)) = 4
((4 * -4 + 6x * -4) + 7x * (4 + 6x)) = 4
((-16 + -24x) + 7x * (4 + 6x)) = 4
(-16 + -24x + (4 * 7x + 6x * 7x)) = 4
(-16 + -24x + (28x + 42x2)) = 4

Combine like terms: -24x + 28x = 4x
(-16 + 4x + 42x2) = 4

Solving
-16 + 4x + 42x2 = 4

Solving for variable 'x'.

Reorder the terms:
-16 + -4 + 4x + 42x2 = 4 + -4

Combine like terms: -16 + -4 = -20
-20 + 4x + 42x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-20 + 4x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 2x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + 2x + 21x2)' equal to zero and attempt to solve:

Simplifying
-10 + 2x + 21x2 = 0

Solving
-10 + 2x + 21x2 = 0

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

Divide each side by '21'.
-0.4761904762 + 0.09523809524x + x2 = 0

Move the constant term to the right:

Add '0.4761904762' to each side of the equation.
-0.4761904762 + 0.09523809524x + 0.4761904762 + x2 = 0 + 0.4761904762

Reorder the terms:
-0.4761904762 + 0.4761904762 + 0.09523809524x + x2 = 0 + 0.4761904762

Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000
0.0000000000 + 0.09523809524x + x2 = 0 + 0.4761904762
0.09523809524x + x2 = 0 + 0.4761904762

Combine like terms: 0 + 0.4761904762 = 0.4761904762
0.09523809524x + x2 = 0.4761904762

The x term is 0.09523809524x.  Take half its coefficient (0.04761904762).
Square it (0.002267573696) and add it to both sides.

Add '0.002267573696' to each side of the equation.
0.09523809524x + 0.002267573696 + x2 = 0.4761904762 + 0.002267573696

Reorder the terms:
0.002267573696 + 0.09523809524x + x2 = 0.4761904762 + 0.002267573696

Combine like terms: 0.4761904762 + 0.002267573696 = 0.478458049896
0.002267573696 + 0.09523809524x + x2 = 0.478458049896

Factor a perfect square on the left side:
(x + 0.04761904762)(x + 0.04761904762) = 0.478458049896

Calculate the square root of the right side: 0.691706621

Break this problem into two subproblems by setting 
(x + 0.04761904762) equal to 0.691706621 and -0.691706621.

Subproblem 1
x + 0.04761904762 = 0.691706621

Simplifying
x + 0.04761904762 = 0.691706621

Reorder the terms:
0.04761904762 + x = 0.691706621

Solving
0.04761904762 + x = 0.691706621

Solving for variable 'x'.

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

Add '-0.04761904762' to each side of the equation.
0.04761904762 + -0.04761904762 + x = 0.691706621 + -0.04761904762

Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000
0.00000000000 + x = 0.691706621 + -0.04761904762
x = 0.691706621 + -0.04761904762

Combine like terms: 0.691706621 + -0.04761904762 = 0.64408757338
x = 0.64408757338

Simplifying
x = 0.64408757338

Subproblem 2
x + 0.04761904762 = -0.691706621

Simplifying
x + 0.04761904762 = -0.691706621

Reorder the terms:
0.04761904762 + x = -0.691706621

Solving
0.04761904762 + x = -0.691706621

Solving for variable 'x'.

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

Add '-0.04761904762' to each side of the equation.
0.04761904762 + -0.04761904762 + x = -0.691706621 + -0.04761904762

Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000
0.00000000000 + x = -0.691706621 + -0.04761904762
x = -0.691706621 + -0.04761904762

Combine like terms: -0.691706621 + -0.04761904762 = -0.73932566862
x = -0.73932566862

Simplifying
x = -0.73932566862

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.64408757338, -0.73932566862}
Solution
x = {0.64408757338, -0.73932566862}