(x-1)(3x-2)=(x+6)(2x+1)

Solution for (x-1)(3x-2)=(x+6)(2x+1) equation:

Simplifying
(x + -1)(3x + -2) = (x + 6)(2x + 1)

Reorder the terms:
(-1 + x)(3x + -2) = (x + 6)(2x + 1)

Reorder the terms:
(-1 + x)(-2 + 3x) = (x + 6)(2x + 1)

Multiply (-1 + x) * (-2 + 3x)
(-1(-2 + 3x) + x(-2 + 3x)) = (x + 6)(2x + 1)
((-2 * -1 + 3x * -1) + x(-2 + 3x)) = (x + 6)(2x + 1)
((2 + -3x) + x(-2 + 3x)) = (x + 6)(2x + 1)
(2 + -3x + (-2 * x + 3x * x)) = (x + 6)(2x + 1)
(2 + -3x + (-2x + 3x2)) = (x + 6)(2x + 1)

Combine like terms: -3x + -2x = -5x
(2 + -5x + 3x2) = (x + 6)(2x + 1)

Reorder the terms:
2 + -5x + 3x2 = (6 + x)(2x + 1)

Reorder the terms:
2 + -5x + 3x2 = (6 + x)(1 + 2x)

Multiply (6 + x) * (1 + 2x)
2 + -5x + 3x2 = (6(1 + 2x) + x(1 + 2x))
2 + -5x + 3x2 = ((1 * 6 + 2x * 6) + x(1 + 2x))
2 + -5x + 3x2 = ((6 + 12x) + x(1 + 2x))
2 + -5x + 3x2 = (6 + 12x + (1 * x + 2x * x))
2 + -5x + 3x2 = (6 + 12x + (1x + 2x2))

Combine like terms: 12x + 1x = 13x
2 + -5x + 3x2 = (6 + 13x + 2x2)

Solving
2 + -5x + 3x2 = 6 + 13x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + -6 + -5x + -13x + 3x2 + -2x2 = 6 + 13x + 2x2 + -6 + -13x + -2x2

Combine like terms: 2 + -6 = -4
-4 + -5x + -13x + 3x2 + -2x2 = 6 + 13x + 2x2 + -6 + -13x + -2x2

Combine like terms: -5x + -13x = -18x
-4 + -18x + 3x2 + -2x2 = 6 + 13x + 2x2 + -6 + -13x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-4 + -18x + 1x2 = 6 + 13x + 2x2 + -6 + -13x + -2x2

Reorder the terms:
-4 + -18x + 1x2 = 6 + -6 + 13x + -13x + 2x2 + -2x2

Combine like terms: 6 + -6 = 0
-4 + -18x + 1x2 = 0 + 13x + -13x + 2x2 + -2x2
-4 + -18x + 1x2 = 13x + -13x + 2x2 + -2x2

Combine like terms: 13x + -13x = 0
-4 + -18x + 1x2 = 0 + 2x2 + -2x2
-4 + -18x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + -18x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -18x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -18x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -18x + x2 = 0 + 4
-18x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-18x + x2 = 4

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 4 + 81

Reorder the terms:
81 + -18x + x2 = 4 + 81

Combine like terms: 4 + 81 = 85
81 + -18x + x2 = 85

Factor a perfect square on the left side:
(x + -9)(x + -9) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + -9) equal to 9.219544457 and -9.219544457.

Subproblem 1
x + -9 = 9.219544457

Simplifying
x + -9 = 9.219544457

Reorder the terms:
-9 + x = 9.219544457

Solving
-9 + x = 9.219544457

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 9.219544457 + 9

Combine like terms: -9 + 9 = 0
0 + x = 9.219544457 + 9
x = 9.219544457 + 9

Combine like terms: 9.219544457 + 9 = 18.219544457
x = 18.219544457

Simplifying
x = 18.219544457

Subproblem 2
x + -9 = -9.219544457

Simplifying
x + -9 = -9.219544457

Reorder the terms:
-9 + x = -9.219544457

Solving
-9 + x = -9.219544457

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -9.219544457 + 9

Combine like terms: -9 + 9 = 0
0 + x = -9.219544457 + 9
x = -9.219544457 + 9

Combine like terms: -9.219544457 + 9 = -0.219544457
x = -0.219544457

Simplifying
x = -0.219544457

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.219544457, -0.219544457}