(28x+6)(32x-6)=x

Solution for (28x+6)(32x-6)=x equation:

Simplifying
(28x + 6)(32x + -6) = x

Reorder the terms:
(6 + 28x)(32x + -6) = x

Reorder the terms:
(6 + 28x)(-6 + 32x) = x

Multiply (6 + 28x) * (-6 + 32x)
(6(-6 + 32x) + 28x * (-6 + 32x)) = x
((-6 * 6 + 32x * 6) + 28x * (-6 + 32x)) = x
((-36 + 192x) + 28x * (-6 + 32x)) = x
(-36 + 192x + (-6 * 28x + 32x * 28x)) = x
(-36 + 192x + (-168x + 896x2)) = x

Combine like terms: 192x + -168x = 24x
(-36 + 24x + 896x2) = x

Solving
-36 + 24x + 896x2 = x

Solving for variable 'x'.

Reorder the terms:
-36 + 24x + -1x + 896x2 = x + -1x

Combine like terms: 24x + -1x = 23x
-36 + 23x + 896x2 = x + -1x

Combine like terms: x + -1x = 0
-36 + 23x + 896x2 = 0

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

Divide each side by '896'.
-0.04017857143 + 0.02566964286x + x2 = 0

Move the constant term to the right:

Add '0.04017857143' to each side of the equation.
-0.04017857143 + 0.02566964286x + 0.04017857143 + x2 = 0 + 0.04017857143

Reorder the terms:
-0.04017857143 + 0.04017857143 + 0.02566964286x + x2 = 0 + 0.04017857143

Combine like terms: -0.04017857143 + 0.04017857143 = 0.00000000000
0.00000000000 + 0.02566964286x + x2 = 0 + 0.04017857143
0.02566964286x + x2 = 0 + 0.04017857143

Combine like terms: 0 + 0.04017857143 = 0.04017857143
0.02566964286x + x2 = 0.04017857143

The x term is 0.02566964286x.  Take half its coefficient (0.01283482143).
Square it (0.0001647326411) and add it to both sides.

Add '0.0001647326411' to each side of the equation.
0.02566964286x + 0.0001647326411 + x2 = 0.04017857143 + 0.0001647326411

Reorder the terms:
0.0001647326411 + 0.02566964286x + x2 = 0.04017857143 + 0.0001647326411

Combine like terms: 0.04017857143 + 0.0001647326411 = 0.0403433040711
0.0001647326411 + 0.02566964286x + x2 = 0.0403433040711

Factor a perfect square on the left side:
(x + 0.01283482143)(x + 0.01283482143) = 0.0403433040711

Calculate the square root of the right side: 0.200856427

Break this problem into two subproblems by setting 
(x + 0.01283482143) equal to 0.200856427 and -0.200856427.

Subproblem 1
x + 0.01283482143 = 0.200856427

Simplifying
x + 0.01283482143 = 0.200856427

Reorder the terms:
0.01283482143 + x = 0.200856427

Solving
0.01283482143 + x = 0.200856427

Solving for variable 'x'.

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

Add '-0.01283482143' to each side of the equation.
0.01283482143 + -0.01283482143 + x = 0.200856427 + -0.01283482143

Combine like terms: 0.01283482143 + -0.01283482143 = 0.00000000000
0.00000000000 + x = 0.200856427 + -0.01283482143
x = 0.200856427 + -0.01283482143

Combine like terms: 0.200856427 + -0.01283482143 = 0.18802160557
x = 0.18802160557

Simplifying
x = 0.18802160557

Subproblem 2
x + 0.01283482143 = -0.200856427

Simplifying
x + 0.01283482143 = -0.200856427

Reorder the terms:
0.01283482143 + x = -0.200856427

Solving
0.01283482143 + x = -0.200856427

Solving for variable 'x'.

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

Add '-0.01283482143' to each side of the equation.
0.01283482143 + -0.01283482143 + x = -0.200856427 + -0.01283482143

Combine like terms: 0.01283482143 + -0.01283482143 = 0.00000000000
0.00000000000 + x = -0.200856427 + -0.01283482143
x = -0.200856427 + -0.01283482143

Combine like terms: -0.200856427 + -0.01283482143 = -0.21369124843
x = -0.21369124843

Simplifying
x = -0.21369124843

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.18802160557, -0.21369124843}