6x+6x*6x=180

Solution for 6x+6x*6x=180 equation:

Simplifying
6x + 6x * 6x = 180

Reorder the terms for easier multiplication:
6x + 6 * 6x * x = 180

Multiply 6 * 6
6x + 36x * x = 180

Multiply x * x
6x + 36x2 = 180

Solving
6x + 36x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 6x + 36x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 6x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + x + 6x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-30 + x + 6x2)' equal to zero and attempt to solve:

Simplifying
-30 + x + 6x2 = 0

Solving
-30 + x + 6x2 = 0

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

Divide each side by '6'.
-5 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 0.1666666667x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 0.1666666667x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 0.1666666667x + x2 = 0 + 5
0.1666666667x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
0.1666666667x + x2 = 5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + 0.1666666667x + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + 0.5 = 2.291287847

Simplifying
x + 0.5 = 2.291287847

Reorder the terms:
0.5 + x = 2.291287847

Solving
0.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.291287847 + -0.5
x = 2.291287847 + -0.5

Combine like terms: 2.291287847 + -0.5 = 1.791287847
x = 1.791287847

Simplifying
x = 1.791287847

Subproblem 2
x + 0.5 = -2.291287847

Simplifying
x + 0.5 = -2.291287847

Reorder the terms:
0.5 + x = -2.291287847

Solving
0.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.291287847 + -0.5
x = -2.291287847 + -0.5

Combine like terms: -2.291287847 + -0.5 = -2.791287847
x = -2.791287847

Simplifying
x = -2.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.791287847, -2.791287847}
Solution
x = {1.791287847, -2.791287847}