(10x+x-1)(x-1)=(x+3)(x+3)

Solution for (10x+x-1)(x-1)=(x+3)(x+3) equation:

Simplifying
(10x + x + -1)(x + -1) = (x + 3)(x + 3)

Reorder the terms:
(-1 + 10x + x)(x + -1) = (x + 3)(x + 3)

Combine like terms: 10x + x = 11x
(-1 + 11x)(x + -1) = (x + 3)(x + 3)

Reorder the terms:
(-1 + 11x)(-1 + x) = (x + 3)(x + 3)

Multiply (-1 + 11x) * (-1 + x)
(-1(-1 + x) + 11x * (-1 + x)) = (x + 3)(x + 3)
((-1 * -1 + x * -1) + 11x * (-1 + x)) = (x + 3)(x + 3)
((1 + -1x) + 11x * (-1 + x)) = (x + 3)(x + 3)
(1 + -1x + (-1 * 11x + x * 11x)) = (x + 3)(x + 3)
(1 + -1x + (-11x + 11x2)) = (x + 3)(x + 3)

Combine like terms: -1x + -11x = -12x
(1 + -12x + 11x2) = (x + 3)(x + 3)

Reorder the terms:
1 + -12x + 11x2 = (3 + x)(x + 3)

Reorder the terms:
1 + -12x + 11x2 = (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
1 + -12x + 11x2 = (3(3 + x) + x(3 + x))
1 + -12x + 11x2 = ((3 * 3 + x * 3) + x(3 + x))
1 + -12x + 11x2 = ((9 + 3x) + x(3 + x))
1 + -12x + 11x2 = (9 + 3x + (3 * x + x * x))
1 + -12x + 11x2 = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
1 + -12x + 11x2 = (9 + 6x + x2)

Solving
1 + -12x + 11x2 = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -9 + -12x + -6x + 11x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 1 + -9 = -8
-8 + -12x + -6x + 11x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: -12x + -6x = -18x
-8 + -18x + 11x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 11x2 + -1x2 = 10x2
-8 + -18x + 10x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
-8 + -18x + 10x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-8 + -18x + 10x2 = 0 + 6x + -6x + x2 + -1x2
-8 + -18x + 10x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-8 + -18x + 10x2 = 0 + x2 + -1x2
-8 + -18x + 10x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -18x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -9x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -9x + 5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -9x + 5x2 = 0

Solving
-4 + -9x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + -1.8x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.8x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.8x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.8x + x2 = 0 + 0.8
-1.8x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.8x + x2 = 0.8

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = 0.8 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = 0.8 + 0.81

Combine like terms: 0.8 + 0.81 = 1.61
0.81 + -1.8x + x2 = 1.61

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 1.61

Calculate the square root of the right side: 1.268857754

Break this problem into two subproblems by setting 
(x + -0.9) equal to 1.268857754 and -1.268857754.

Subproblem 1
x + -0.9 = 1.268857754

Simplifying
x + -0.9 = 1.268857754

Reorder the terms:
-0.9 + x = 1.268857754

Solving
-0.9 + x = 1.268857754

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = 1.268857754 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = 1.268857754 + 0.9
x = 1.268857754 + 0.9

Combine like terms: 1.268857754 + 0.9 = 2.168857754
x = 2.168857754

Simplifying
x = 2.168857754

Subproblem 2
x + -0.9 = -1.268857754

Simplifying
x + -0.9 = -1.268857754

Reorder the terms:
-0.9 + x = -1.268857754

Solving
-0.9 + x = -1.268857754

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = -1.268857754 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = -1.268857754 + 0.9
x = -1.268857754 + 0.9

Combine like terms: -1.268857754 + 0.9 = -0.368857754
x = -0.368857754

Simplifying
x = -0.368857754

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.168857754, -0.368857754}
Solution
x = {2.168857754, -0.368857754}