2x+3*27x*2x=3

Solution for 2x+3*27x*2x=3 equation:

Simplifying
2x + 3 * 27x * 2x = 3

Reorder the terms for easier multiplication:
2x + 3 * 27 * 2x * x = 3

Multiply 3 * 27
2x + 81 * 2x * x = 3

Multiply 81 * 2
2x + 162x * x = 3

Multiply x * x
2x + 162x2 = 3

Solving
2x + 162x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 2x + 162x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 2x + 162x2 = 0

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

Divide each side by '162'.
-0.01851851852 + 0.01234567901x + x2 = 0

Move the constant term to the right:

Add '0.01851851852' to each side of the equation.
-0.01851851852 + 0.01234567901x + 0.01851851852 + x2 = 0 + 0.01851851852

Reorder the terms:
-0.01851851852 + 0.01851851852 + 0.01234567901x + x2 = 0 + 0.01851851852

Combine like terms: -0.01851851852 + 0.01851851852 = 0.00000000000
0.00000000000 + 0.01234567901x + x2 = 0 + 0.01851851852
0.01234567901x + x2 = 0 + 0.01851851852

Combine like terms: 0 + 0.01851851852 = 0.01851851852
0.01234567901x + x2 = 0.01851851852

The x term is 0.01234567901x.  Take half its coefficient (0.006172839505).
Square it (0.00003810394755) and add it to both sides.

Add '0.00003810394755' to each side of the equation.
0.01234567901x + 0.00003810394755 + x2 = 0.01851851852 + 0.00003810394755

Reorder the terms:
0.00003810394755 + 0.01234567901x + x2 = 0.01851851852 + 0.00003810394755

Combine like terms: 0.01851851852 + 0.00003810394755 = 0.01855662246755
0.00003810394755 + 0.01234567901x + x2 = 0.01855662246755

Factor a perfect square on the left side:
(x + 0.006172839505)(x + 0.006172839505) = 0.01855662246755

Calculate the square root of the right side: 0.136222694

Break this problem into two subproblems by setting 
(x + 0.006172839505) equal to 0.136222694 and -0.136222694.

Subproblem 1
x + 0.006172839505 = 0.136222694

Simplifying
x + 0.006172839505 = 0.136222694

Reorder the terms:
0.006172839505 + x = 0.136222694

Solving
0.006172839505 + x = 0.136222694

Solving for variable 'x'.

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

Add '-0.006172839505' to each side of the equation.
0.006172839505 + -0.006172839505 + x = 0.136222694 + -0.006172839505

Combine like terms: 0.006172839505 + -0.006172839505 = 0.000000000000
0.000000000000 + x = 0.136222694 + -0.006172839505
x = 0.136222694 + -0.006172839505

Combine like terms: 0.136222694 + -0.006172839505 = 0.130049854495
x = 0.130049854495

Simplifying
x = 0.130049854495

Subproblem 2
x + 0.006172839505 = -0.136222694

Simplifying
x + 0.006172839505 = -0.136222694

Reorder the terms:
0.006172839505 + x = -0.136222694

Solving
0.006172839505 + x = -0.136222694

Solving for variable 'x'.

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

Add '-0.006172839505' to each side of the equation.
0.006172839505 + -0.006172839505 + x = -0.136222694 + -0.006172839505

Combine like terms: 0.006172839505 + -0.006172839505 = 0.000000000000
0.000000000000 + x = -0.136222694 + -0.006172839505
x = -0.136222694 + -0.006172839505

Combine like terms: -0.136222694 + -0.006172839505 = -0.142395533505
x = -0.142395533505

Simplifying
x = -0.142395533505

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.130049854495, -0.142395533505}