(12x-10)(12x+10)=x

Solution for (12x-10)(12x+10)=x equation:

Simplifying
(12x + -10)(12x + 10) = x

Reorder the terms:
(-10 + 12x)(12x + 10) = x

Reorder the terms:
(-10 + 12x)(10 + 12x) = x

Multiply (-10 + 12x) * (10 + 12x)
(-10(10 + 12x) + 12x * (10 + 12x)) = x
((10 * -10 + 12x * -10) + 12x * (10 + 12x)) = x
((-100 + -120x) + 12x * (10 + 12x)) = x
(-100 + -120x + (10 * 12x + 12x * 12x)) = x
(-100 + -120x + (120x + 144x2)) = x

Combine like terms: -120x + 120x = 0
(-100 + 0 + 144x2) = x
(-100 + 144x2) = x

Solving
-100 + 144x2 = x

Solving for variable 'x'.

Reorder the terms:
-100 + -1x + 144x2 = x + -1x

Combine like terms: x + -1x = 0
-100 + -1x + 144x2 = 0

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

Divide each side by '144'.
-0.6944444444 + -0.006944444444x + x2 = 0

Move the constant term to the right:

Add '0.6944444444' to each side of the equation.
-0.6944444444 + -0.006944444444x + 0.6944444444 + x2 = 0 + 0.6944444444

Reorder the terms:
-0.6944444444 + 0.6944444444 + -0.006944444444x + x2 = 0 + 0.6944444444

Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000
0.0000000000 + -0.006944444444x + x2 = 0 + 0.6944444444
-0.006944444444x + x2 = 0 + 0.6944444444

Combine like terms: 0 + 0.6944444444 = 0.6944444444
-0.006944444444x + x2 = 0.6944444444

The x term is -0.006944444444x.  Take half its coefficient (-0.003472222222).
Square it (0.00001205632716) and add it to both sides.

Add '0.00001205632716' to each side of the equation.
-0.006944444444x + 0.00001205632716 + x2 = 0.6944444444 + 0.00001205632716

Reorder the terms:
0.00001205632716 + -0.006944444444x + x2 = 0.6944444444 + 0.00001205632716

Combine like terms: 0.6944444444 + 0.00001205632716 = 0.69445650072716
0.00001205632716 + -0.006944444444x + x2 = 0.69445650072716

Factor a perfect square on the left side:
(x + -0.003472222222)(x + -0.003472222222) = 0.69445650072716

Calculate the square root of the right side: 0.833340567

Break this problem into two subproblems by setting 
(x + -0.003472222222) equal to 0.833340567 and -0.833340567.

Subproblem 1
x + -0.003472222222 = 0.833340567

Simplifying
x + -0.003472222222 = 0.833340567

Reorder the terms:
-0.003472222222 + x = 0.833340567

Solving
-0.003472222222 + x = 0.833340567

Solving for variable 'x'.

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

Add '0.003472222222' to each side of the equation.
-0.003472222222 + 0.003472222222 + x = 0.833340567 + 0.003472222222

Combine like terms: -0.003472222222 + 0.003472222222 = 0.000000000000
0.000000000000 + x = 0.833340567 + 0.003472222222
x = 0.833340567 + 0.003472222222

Combine like terms: 0.833340567 + 0.003472222222 = 0.836812789222
x = 0.836812789222

Simplifying
x = 0.836812789222

Subproblem 2
x + -0.003472222222 = -0.833340567

Simplifying
x + -0.003472222222 = -0.833340567

Reorder the terms:
-0.003472222222 + x = -0.833340567

Solving
-0.003472222222 + x = -0.833340567

Solving for variable 'x'.

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

Add '0.003472222222' to each side of the equation.
-0.003472222222 + 0.003472222222 + x = -0.833340567 + 0.003472222222

Combine like terms: -0.003472222222 + 0.003472222222 = 0.000000000000
0.000000000000 + x = -0.833340567 + 0.003472222222
x = -0.833340567 + 0.003472222222

Combine like terms: -0.833340567 + 0.003472222222 = -0.829868344778
x = -0.829868344778

Simplifying
x = -0.829868344778

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.836812789222, -0.829868344778}