(3x-2)(x-1)=18x+4

Solution for (3x-2)(x-1)=18x+4 equation:

Simplifying
(3x + -2)(x + -1) = 18x + 4

Reorder the terms:
(-2 + 3x)(x + -1) = 18x + 4

Reorder the terms:
(-2 + 3x)(-1 + x) = 18x + 4

Multiply (-2 + 3x) * (-1 + x)
(-2(-1 + x) + 3x * (-1 + x)) = 18x + 4
((-1 * -2 + x * -2) + 3x * (-1 + x)) = 18x + 4
((2 + -2x) + 3x * (-1 + x)) = 18x + 4
(2 + -2x + (-1 * 3x + x * 3x)) = 18x + 4
(2 + -2x + (-3x + 3x2)) = 18x + 4

Combine like terms: -2x + -3x = -5x
(2 + -5x + 3x2) = 18x + 4

Reorder the terms:
2 + -5x + 3x2 = 4 + 18x

Solving
2 + -5x + 3x2 = 4 + 18x

Solving for variable 'x'.

Reorder the terms:
2 + -4 + -5x + -18x + 3x2 = 4 + 18x + -4 + -18x

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

Combine like terms: -5x + -18x = -23x
-2 + -23x + 3x2 = 4 + 18x + -4 + -18x

Reorder the terms:
-2 + -23x + 3x2 = 4 + -4 + 18x + -18x

Combine like terms: 4 + -4 = 0
-2 + -23x + 3x2 = 0 + 18x + -18x
-2 + -23x + 3x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-2 + -23x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + -7.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -7.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -7.666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -7.666666667x + x2 = 0 + 0.6666666667
-7.666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-7.666666667x + x2 = 0.6666666667

The x term is -7.666666667x.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667x + 14.69444445 + x2 = 0.6666666667 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667x + x2 = 0.6666666667 + 14.69444445

Combine like terms: 0.6666666667 + 14.69444445 = 15.3611111167
14.69444445 + -7.666666667x + x2 = 15.3611111167

Factor a perfect square on the left side:
(x + -3.833333334)(x + -3.833333334) = 15.3611111167

Calculate the square root of the right side: 3.919325339

Break this problem into two subproblems by setting 
(x + -3.833333334) equal to 3.919325339 and -3.919325339.

Subproblem 1
x + -3.833333334 = 3.919325339

Simplifying
x + -3.833333334 = 3.919325339

Reorder the terms:
-3.833333334 + x = 3.919325339

Solving
-3.833333334 + x = 3.919325339

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = 3.919325339 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = 3.919325339 + 3.833333334
x = 3.919325339 + 3.833333334

Combine like terms: 3.919325339 + 3.833333334 = 7.752658673
x = 7.752658673

Simplifying
x = 7.752658673

Subproblem 2
x + -3.833333334 = -3.919325339

Simplifying
x + -3.833333334 = -3.919325339

Reorder the terms:
-3.833333334 + x = -3.919325339

Solving
-3.833333334 + x = -3.919325339

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = -3.919325339 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = -3.919325339 + 3.833333334
x = -3.919325339 + 3.833333334

Combine like terms: -3.919325339 + 3.833333334 = -0.085992005
x = -0.085992005

Simplifying
x = -0.085992005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.752658673, -0.085992005}