(3x-2)=(x-5)(9x+4)

Solution for (3x-2)=(x-5)(9x+4) equation:

Simplifying
(3x + -2) = (x + -5)(9x + 4)

Reorder the terms:
(-2 + 3x) = (x + -5)(9x + 4)

Remove parenthesis around (-2 + 3x)
-2 + 3x = (x + -5)(9x + 4)

Reorder the terms:
-2 + 3x = (-5 + x)(9x + 4)

Reorder the terms:
-2 + 3x = (-5 + x)(4 + 9x)

Multiply (-5 + x) * (4 + 9x)
-2 + 3x = (-5(4 + 9x) + x(4 + 9x))
-2 + 3x = ((4 * -5 + 9x * -5) + x(4 + 9x))
-2 + 3x = ((-20 + -45x) + x(4 + 9x))
-2 + 3x = (-20 + -45x + (4 * x + 9x * x))
-2 + 3x = (-20 + -45x + (4x + 9x2))

Combine like terms: -45x + 4x = -41x
-2 + 3x = (-20 + -41x + 9x2)

Solving
-2 + 3x = -20 + -41x + 9x2

Solving for variable 'x'.

Reorder the terms:
-2 + 20 + 3x + 41x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Combine like terms: -2 + 20 = 18
18 + 3x + 41x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Combine like terms: 3x + 41x = 44x
18 + 44x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Reorder the terms:
18 + 44x + -9x2 = -20 + 20 + -41x + 41x + 9x2 + -9x2

Combine like terms: -20 + 20 = 0
18 + 44x + -9x2 = 0 + -41x + 41x + 9x2 + -9x2
18 + 44x + -9x2 = -41x + 41x + 9x2 + -9x2

Combine like terms: -41x + 41x = 0
18 + 44x + -9x2 = 0 + 9x2 + -9x2
18 + 44x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
18 + 44x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-2 + -4.888888889x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4.888888889x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -4.888888889x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4.888888889x + x2 = 0 + 2
-4.888888889x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4.888888889x + x2 = 2

The x term is -4.888888889x.  Take half its coefficient (-2.444444445).
Square it (5.975308645) and add it to both sides.

Add '5.975308645' to each side of the equation.
-4.888888889x + 5.975308645 + x2 = 2 + 5.975308645

Reorder the terms:
5.975308645 + -4.888888889x + x2 = 2 + 5.975308645

Combine like terms: 2 + 5.975308645 = 7.975308645
5.975308645 + -4.888888889x + x2 = 7.975308645

Factor a perfect square on the left side:
(x + -2.444444445)(x + -2.444444445) = 7.975308645

Calculate the square root of the right side: 2.824058895

Break this problem into two subproblems by setting 
(x + -2.444444445) equal to 2.824058895 and -2.824058895.

Subproblem 1
x + -2.444444445 = 2.824058895

Simplifying
x + -2.444444445 = 2.824058895

Reorder the terms:
-2.444444445 + x = 2.824058895

Solving
-2.444444445 + x = 2.824058895

Solving for variable 'x'.

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

Add '2.444444445' to each side of the equation.
-2.444444445 + 2.444444445 + x = 2.824058895 + 2.444444445

Combine like terms: -2.444444445 + 2.444444445 = 0.000000000
0.000000000 + x = 2.824058895 + 2.444444445
x = 2.824058895 + 2.444444445

Combine like terms: 2.824058895 + 2.444444445 = 5.26850334
x = 5.26850334

Simplifying
x = 5.26850334

Subproblem 2
x + -2.444444445 = -2.824058895

Simplifying
x + -2.444444445 = -2.824058895

Reorder the terms:
-2.444444445 + x = -2.824058895

Solving
-2.444444445 + x = -2.824058895

Solving for variable 'x'.

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

Add '2.444444445' to each side of the equation.
-2.444444445 + 2.444444445 + x = -2.824058895 + 2.444444445

Combine like terms: -2.444444445 + 2.444444445 = 0.000000000
0.000000000 + x = -2.824058895 + 2.444444445
x = -2.824058895 + 2.444444445

Combine like terms: -2.824058895 + 2.444444445 = -0.37961445
x = -0.37961445

Simplifying
x = -0.37961445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.26850334, -0.37961445}