(10x-2)(x-1)=10

Solution for (10x-2)(x-1)=10 equation:

Simplifying
(10x + -2)(x + -1) = 10

Reorder the terms:
(-2 + 10x)(x + -1) = 10

Reorder the terms:
(-2 + 10x)(-1 + x) = 10

Multiply (-2 + 10x) * (-1 + x)
(-2(-1 + x) + 10x * (-1 + x)) = 10
((-1 * -2 + x * -2) + 10x * (-1 + x)) = 10
((2 + -2x) + 10x * (-1 + x)) = 10
(2 + -2x + (-1 * 10x + x * 10x)) = 10
(2 + -2x + (-10x + 10x2)) = 10

Combine like terms: -2x + -10x = -12x
(2 + -12x + 10x2) = 10

Solving
2 + -12x + 10x2 = 10

Solving for variable 'x'.

Reorder the terms:
2 + -10 + -12x + 10x2 = 10 + -10

Combine like terms: 2 + -10 = -8
-8 + -12x + 10x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-8 + -12x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -6x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -6x + 5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -6x + 5x2 = 0

Solving
-4 + -6x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + -1.2x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.2x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.2x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.2x + x2 = 0 + 0.8
-1.2x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.2x + x2 = 0.8

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 0.8 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 0.8 + 0.36

Combine like terms: 0.8 + 0.36 = 1.16
0.36 + -1.2x + x2 = 1.16

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.077032961 and -1.077032961.

Subproblem 1
x + -0.6 = 1.077032961

Simplifying
x + -0.6 = 1.077032961

Reorder the terms:
-0.6 + x = 1.077032961

Solving
-0.6 + x = 1.077032961

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 1.077032961 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 1.077032961 + 0.6
x = 1.077032961 + 0.6

Combine like terms: 1.077032961 + 0.6 = 1.677032961
x = 1.677032961

Simplifying
x = 1.677032961

Subproblem 2
x + -0.6 = -1.077032961

Simplifying
x + -0.6 = -1.077032961

Reorder the terms:
-0.6 + x = -1.077032961

Solving
-0.6 + x = -1.077032961

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -1.077032961 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -1.077032961 + 0.6
x = -1.077032961 + 0.6

Combine like terms: -1.077032961 + 0.6 = -0.477032961
x = -0.477032961

Simplifying
x = -0.477032961

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.677032961, -0.477032961}
Solution
x = {1.677032961, -0.477032961}