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

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

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

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

Reorder the terms for easier multiplication:
2(-2 + 3x) = (x + -5)(9x + 4)
(-2 * 2 + 3x * 2) = (x + -5)(9x + 4)
(-4 + 6x) = (x + -5)(9x + 4)

Reorder the terms:
-4 + 6x = (-5 + x)(9x + 4)

Reorder the terms:
-4 + 6x = (-5 + x)(4 + 9x)

Multiply (-5 + x) * (4 + 9x)
-4 + 6x = (-5(4 + 9x) + x(4 + 9x))
-4 + 6x = ((4 * -5 + 9x * -5) + x(4 + 9x))
-4 + 6x = ((-20 + -45x) + x(4 + 9x))
-4 + 6x = (-20 + -45x + (4 * x + 9x * x))
-4 + 6x = (-20 + -45x + (4x + 9x2))

Combine like terms: -45x + 4x = -41x
-4 + 6x = (-20 + -41x + 9x2)

Solving
-4 + 6x = -20 + -41x + 9x2

Solving for variable 'x'.

Reorder the terms:
-4 + 20 + 6x + 41x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Combine like terms: -4 + 20 = 16
16 + 6x + 41x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Combine like terms: 6x + 41x = 47x
16 + 47x + -9x2 = -20 + -41x + 9x2 + 20 + 41x + -9x2

Reorder the terms:
16 + 47x + -9x2 = -20 + 20 + -41x + 41x + 9x2 + -9x2

Combine like terms: -20 + 20 = 0
16 + 47x + -9x2 = 0 + -41x + 41x + 9x2 + -9x2
16 + 47x + -9x2 = -41x + 41x + 9x2 + -9x2

Combine like terms: -41x + 41x = 0
16 + 47x + -9x2 = 0 + 9x2 + -9x2
16 + 47x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
16 + 47x + -9x2 = 0

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

Divide each side by '-9'.
-1.777777778 + -5.222222222x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -5.222222222x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -5.222222222x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -5.222222222x + x2 = 0 + 1.777777778
-5.222222222x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-5.222222222x + x2 = 1.777777778

The x term is -5.222222222x.  Take half its coefficient (-2.611111111).
Square it (6.817901234) and add it to both sides.

Add '6.817901234' to each side of the equation.
-5.222222222x + 6.817901234 + x2 = 1.777777778 + 6.817901234

Reorder the terms:
6.817901234 + -5.222222222x + x2 = 1.777777778 + 6.817901234

Combine like terms: 1.777777778 + 6.817901234 = 8.595679012
6.817901234 + -5.222222222x + x2 = 8.595679012

Factor a perfect square on the left side:
(x + -2.611111111)(x + -2.611111111) = 8.595679012

Calculate the square root of the right side: 2.931838845

Break this problem into two subproblems by setting 
(x + -2.611111111) equal to 2.931838845 and -2.931838845.

Subproblem 1
x + -2.611111111 = 2.931838845

Simplifying
x + -2.611111111 = 2.931838845

Reorder the terms:
-2.611111111 + x = 2.931838845

Solving
-2.611111111 + x = 2.931838845

Solving for variable 'x'.

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

Add '2.611111111' to each side of the equation.
-2.611111111 + 2.611111111 + x = 2.931838845 + 2.611111111

Combine like terms: -2.611111111 + 2.611111111 = 0.000000000
0.000000000 + x = 2.931838845 + 2.611111111
x = 2.931838845 + 2.611111111

Combine like terms: 2.931838845 + 2.611111111 = 5.542949956
x = 5.542949956

Simplifying
x = 5.542949956

Subproblem 2
x + -2.611111111 = -2.931838845

Simplifying
x + -2.611111111 = -2.931838845

Reorder the terms:
-2.611111111 + x = -2.931838845

Solving
-2.611111111 + x = -2.931838845

Solving for variable 'x'.

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

Add '2.611111111' to each side of the equation.
-2.611111111 + 2.611111111 + x = -2.931838845 + 2.611111111

Combine like terms: -2.611111111 + 2.611111111 = 0.000000000
0.000000000 + x = -2.931838845 + 2.611111111
x = -2.931838845 + 2.611111111

Combine like terms: -2.931838845 + 2.611111111 = -0.320727734
x = -0.320727734

Simplifying
x = -0.320727734

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.542949956, -0.320727734}