81x+12x-4=3x(3x+1)

Solution for 81x+12x-4=3x(3x+1) equation:

Simplifying
81x + 12x + -4 = 3x(3x + 1)

Reorder the terms:
-4 + 81x + 12x = 3x(3x + 1)

Combine like terms: 81x + 12x = 93x
-4 + 93x = 3x(3x + 1)

Reorder the terms:
-4 + 93x = 3x(1 + 3x)
-4 + 93x = (1 * 3x + 3x * 3x)
-4 + 93x = (3x + 9x2)

Solving
-4 + 93x = 3x + 9x2

Solving for variable 'x'.

Combine like terms: 93x + -3x = 90x
-4 + 90x + -9x2 = 3x + 9x2 + -3x + -9x2

Reorder the terms:
-4 + 90x + -9x2 = 3x + -3x + 9x2 + -9x2

Combine like terms: 3x + -3x = 0
-4 + 90x + -9x2 = 0 + 9x2 + -9x2
-4 + 90x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-4 + 90x + -9x2 = 0

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

Divide each side by '-9'.
0.4444444444 + -10x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -10x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -10x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -10x + x2 = 0 + -0.4444444444
-10x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-10x + x2 = -0.4444444444

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -0.4444444444 + 25

Reorder the terms:
25 + -10x + x2 = -0.4444444444 + 25

Combine like terms: -0.4444444444 + 25 = 24.5555555556
25 + -10x + x2 = 24.5555555556

Factor a perfect square on the left side:
(x + -5)(x + -5) = 24.5555555556

Calculate the square root of the right side: 4.955356249

Break this problem into two subproblems by setting 
(x + -5) equal to 4.955356249 and -4.955356249.

Subproblem 1
x + -5 = 4.955356249

Simplifying
x + -5 = 4.955356249

Reorder the terms:
-5 + x = 4.955356249

Solving
-5 + x = 4.955356249

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.955356249 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.955356249 + 5
x = 4.955356249 + 5

Combine like terms: 4.955356249 + 5 = 9.955356249
x = 9.955356249

Simplifying
x = 9.955356249

Subproblem 2
x + -5 = -4.955356249

Simplifying
x + -5 = -4.955356249

Reorder the terms:
-5 + x = -4.955356249

Solving
-5 + x = -4.955356249

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.955356249 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.955356249 + 5
x = -4.955356249 + 5

Combine like terms: -4.955356249 + 5 = 0.044643751
x = 0.044643751

Simplifying
x = 0.044643751

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.955356249, 0.044643751}