3(x-6)(2.3x-6)=600

Solution for 3(x-6)(2.3x-6)=600 equation:

Simplifying
3(x + -6)(2.3x + -6) = 600

Reorder the terms:
3(-6 + x)(2.3x + -6) = 600

Reorder the terms:
3(-6 + x)(-6 + 2.3x) = 600

Multiply (-6 + x) * (-6 + 2.3x)
3(-6(-6 + 2.3x) + x(-6 + 2.3x)) = 600
3((-6 * -6 + 2.3x * -6) + x(-6 + 2.3x)) = 600
3((36 + -13.8x) + x(-6 + 2.3x)) = 600
3(36 + -13.8x + (-6 * x + 2.3x * x)) = 600
3(36 + -13.8x + (-6x + 2.3x2)) = 600

Combine like terms: -13.8x + -6x = -19.8x
3(36 + -19.8x + 2.3x2) = 600
(36 * 3 + -19.8x * 3 + 2.3x2 * 3) = 600
(108 + -59.4x + 6.9x2) = 600

Solving
108 + -59.4x + 6.9x2 = 600

Solving for variable 'x'.

Reorder the terms:
108 + -600 + -59.4x + 6.9x2 = 600 + -600

Combine like terms: 108 + -600 = -492
-492 + -59.4x + 6.9x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-492 + -59.4x + 6.9x2 = 0

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

Divide each side by '6.9'.
-71.30434783 + -8.608695652x + x2 = 0

Move the constant term to the right:

Add '71.30434783' to each side of the equation.
-71.30434783 + -8.608695652x + 71.30434783 + x2 = 0 + 71.30434783

Reorder the terms:
-71.30434783 + 71.30434783 + -8.608695652x + x2 = 0 + 71.30434783

Combine like terms: -71.30434783 + 71.30434783 = 0.00000000
0.00000000 + -8.608695652x + x2 = 0 + 71.30434783
-8.608695652x + x2 = 0 + 71.30434783

Combine like terms: 0 + 71.30434783 = 71.30434783
-8.608695652x + x2 = 71.30434783

The x term is -8.608695652x.  Take half its coefficient (-4.304347826).
Square it (18.52741021) and add it to both sides.

Add '18.52741021' to each side of the equation.
-8.608695652x + 18.52741021 + x2 = 71.30434783 + 18.52741021

Reorder the terms:
18.52741021 + -8.608695652x + x2 = 71.30434783 + 18.52741021

Combine like terms: 71.30434783 + 18.52741021 = 89.83175804
18.52741021 + -8.608695652x + x2 = 89.83175804

Factor a perfect square on the left side:
(x + -4.304347826)(x + -4.304347826) = 89.83175804

Calculate the square root of the right side: 9.477961703

Break this problem into two subproblems by setting 
(x + -4.304347826) equal to 9.477961703 and -9.477961703.

Subproblem 1
x + -4.304347826 = 9.477961703

Simplifying
x + -4.304347826 = 9.477961703

Reorder the terms:
-4.304347826 + x = 9.477961703

Solving
-4.304347826 + x = 9.477961703

Solving for variable 'x'.

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

Add '4.304347826' to each side of the equation.
-4.304347826 + 4.304347826 + x = 9.477961703 + 4.304347826

Combine like terms: -4.304347826 + 4.304347826 = 0.000000000
0.000000000 + x = 9.477961703 + 4.304347826
x = 9.477961703 + 4.304347826

Combine like terms: 9.477961703 + 4.304347826 = 13.782309529
x = 13.782309529

Simplifying
x = 13.782309529

Subproblem 2
x + -4.304347826 = -9.477961703

Simplifying
x + -4.304347826 = -9.477961703

Reorder the terms:
-4.304347826 + x = -9.477961703

Solving
-4.304347826 + x = -9.477961703

Solving for variable 'x'.

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

Add '4.304347826' to each side of the equation.
-4.304347826 + 4.304347826 + x = -9.477961703 + 4.304347826

Combine like terms: -4.304347826 + 4.304347826 = 0.000000000
0.000000000 + x = -9.477961703 + 4.304347826
x = -9.477961703 + 4.304347826

Combine like terms: -9.477961703 + 4.304347826 = -5.173613877
x = -5.173613877

Simplifying
x = -5.173613877

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.782309529, -5.173613877}