81x^2+72x+6=0

Solution for 81x^2+72x+6=0 equation:

Simplifying
81x2 + 72x + 6 = 0

Reorder the terms:
6 + 72x + 81x2 = 0

Solving
6 + 72x + 81x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 24x + 27x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 24x + 27x2)' equal to zero and attempt to solve:

Simplifying
2 + 24x + 27x2 = 0

Solving
2 + 24x + 27x2 = 0

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

Divide each side by '27'.
0.07407407407 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '-0.07407407407' to each side of the equation.
0.07407407407 + 0.8888888889x + -0.07407407407 + x2 = 0 + -0.07407407407

Reorder the terms:
0.07407407407 + -0.07407407407 + 0.8888888889x + x2 = 0 + -0.07407407407

Combine like terms: 0.07407407407 + -0.07407407407 = 0.00000000000
0.00000000000 + 0.8888888889x + x2 = 0 + -0.07407407407
0.8888888889x + x2 = 0 + -0.07407407407

Combine like terms: 0 + -0.07407407407 = -0.07407407407
0.8888888889x + x2 = -0.07407407407

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = -0.07407407407 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = -0.07407407407 + 0.1975308642

Combine like terms: -0.07407407407 + 0.1975308642 = 0.12345679013
0.1975308642 + 0.8888888889x + x2 = 0.12345679013

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 0.12345679013

Calculate the square root of the right side: 0.351364184

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 0.351364184 and -0.351364184.

Subproblem 1
x + 0.4444444445 = 0.351364184

Simplifying
x + 0.4444444445 = 0.351364184

Reorder the terms:
0.4444444445 + x = 0.351364184

Solving
0.4444444445 + x = 0.351364184

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = 0.351364184 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 0.351364184 + -0.4444444445
x = 0.351364184 + -0.4444444445

Combine like terms: 0.351364184 + -0.4444444445 = -0.0930802605
x = -0.0930802605

Simplifying
x = -0.0930802605

Subproblem 2
x + 0.4444444445 = -0.351364184

Simplifying
x + 0.4444444445 = -0.351364184

Reorder the terms:
0.4444444445 + x = -0.351364184

Solving
0.4444444445 + x = -0.351364184

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = -0.351364184 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -0.351364184 + -0.4444444445
x = -0.351364184 + -0.4444444445

Combine like terms: -0.351364184 + -0.4444444445 = -0.7958086285
x = -0.7958086285

Simplifying
x = -0.7958086285

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0930802605, -0.7958086285}
Solution
x = {-0.0930802605, -0.7958086285}