3(x-6)(2.7x-6)=

Solution for 3(x-6)(2.7x-6)= equation:

Simplifying
3(x + -6)(2.7x + -6) = 0

Reorder the terms:
3(-6 + x)(2.7x + -6) = 0

Reorder the terms:
3(-6 + x)(-6 + 2.7x) = 0

Multiply (-6 + x) * (-6 + 2.7x)
3(-6(-6 + 2.7x) + x(-6 + 2.7x)) = 0
3((-6 * -6 + 2.7x * -6) + x(-6 + 2.7x)) = 0
3((36 + -16.2x) + x(-6 + 2.7x)) = 0
3(36 + -16.2x + (-6 * x + 2.7x * x)) = 0
3(36 + -16.2x + (-6x + 2.7x2)) = 0

Combine like terms: -16.2x + -6x = -22.2x
3(36 + -22.2x + 2.7x2) = 0
(36 * 3 + -22.2x * 3 + 2.7x2 * 3) = 0
(108 + -66.6x + 8.1x2) = 0

Solving
108 + -66.6x + 8.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '8.1'.
13.33333333 + -8.222222222x + x2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + -8.222222222x + -13.33333333 + x2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + -8.222222222x + x2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + -8.222222222x + x2 = 0 + -13.33333333
-8.222222222x + x2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
-8.222222222x + x2 = -13.33333333

The x term is -8.222222222x.  Take half its coefficient (-4.111111111).
Square it (16.90123457) and add it to both sides.

Add '16.90123457' to each side of the equation.
-8.222222222x + 16.90123457 + x2 = -13.33333333 + 16.90123457

Reorder the terms:
16.90123457 + -8.222222222x + x2 = -13.33333333 + 16.90123457

Combine like terms: -13.33333333 + 16.90123457 = 3.56790124
16.90123457 + -8.222222222x + x2 = 3.56790124

Factor a perfect square on the left side:
(x + -4.111111111)(x + -4.111111111) = 3.56790124

Calculate the square root of the right side: 1.88888889

Break this problem into two subproblems by setting 
(x + -4.111111111) equal to 1.88888889 and -1.88888889.

Subproblem 1
x + -4.111111111 = 1.88888889

Simplifying
x + -4.111111111 = 1.88888889

Reorder the terms:
-4.111111111 + x = 1.88888889

Solving
-4.111111111 + x = 1.88888889

Solving for variable 'x'.

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

Add '4.111111111' to each side of the equation.
-4.111111111 + 4.111111111 + x = 1.88888889 + 4.111111111

Combine like terms: -4.111111111 + 4.111111111 = 0.000000000
0.000000000 + x = 1.88888889 + 4.111111111
x = 1.88888889 + 4.111111111

Combine like terms: 1.88888889 + 4.111111111 = 6.000000001
x = 6.000000001

Simplifying
x = 6.000000001

Subproblem 2
x + -4.111111111 = -1.88888889

Simplifying
x + -4.111111111 = -1.88888889

Reorder the terms:
-4.111111111 + x = -1.88888889

Solving
-4.111111111 + x = -1.88888889

Solving for variable 'x'.

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

Add '4.111111111' to each side of the equation.
-4.111111111 + 4.111111111 + x = -1.88888889 + 4.111111111

Combine like terms: -4.111111111 + 4.111111111 = 0.000000000
0.000000000 + x = -1.88888889 + 4.111111111
x = -1.88888889 + 4.111111111

Combine like terms: -1.88888889 + 4.111111111 = 2.222222221
x = 2.222222221

Simplifying
x = 2.222222221

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.000000001, 2.222222221}