3(x-6)(2.9x-6)=800

Solution for 3(x-6)(2.9x-6)=800 equation:

Simplifying
3(x + -6)(2.9x + -6) = 800

Reorder the terms:
3(-6 + x)(2.9x + -6) = 800

Reorder the terms:
3(-6 + x)(-6 + 2.9x) = 800

Multiply (-6 + x) * (-6 + 2.9x)
3(-6(-6 + 2.9x) + x(-6 + 2.9x)) = 800
3((-6 * -6 + 2.9x * -6) + x(-6 + 2.9x)) = 800
3((36 + -17.4x) + x(-6 + 2.9x)) = 800
3(36 + -17.4x + (-6 * x + 2.9x * x)) = 800
3(36 + -17.4x + (-6x + 2.9x2)) = 800

Combine like terms: -17.4x + -6x = -23.4x
3(36 + -23.4x + 2.9x2) = 800
(36 * 3 + -23.4x * 3 + 2.9x2 * 3) = 800
(108 + -70.2x + 8.7x2) = 800

Solving
108 + -70.2x + 8.7x2 = 800

Solving for variable 'x'.

Reorder the terms:
108 + -800 + -70.2x + 8.7x2 = 800 + -800

Combine like terms: 108 + -800 = -692
-692 + -70.2x + 8.7x2 = 800 + -800

Combine like terms: 800 + -800 = 0
-692 + -70.2x + 8.7x2 = 0

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

Divide each side by '8.7'.
-79.54022989 + -8.068965517x + x2 = 0

Move the constant term to the right:

Add '79.54022989' to each side of the equation.
-79.54022989 + -8.068965517x + 79.54022989 + x2 = 0 + 79.54022989

Reorder the terms:
-79.54022989 + 79.54022989 + -8.068965517x + x2 = 0 + 79.54022989

Combine like terms: -79.54022989 + 79.54022989 = 0.00000000
0.00000000 + -8.068965517x + x2 = 0 + 79.54022989
-8.068965517x + x2 = 0 + 79.54022989

Combine like terms: 0 + 79.54022989 = 79.54022989
-8.068965517x + x2 = 79.54022989

The x term is -8.068965517x.  Take half its coefficient (-4.034482759).
Square it (16.27705113) and add it to both sides.

Add '16.27705113' to each side of the equation.
-8.068965517x + 16.27705113 + x2 = 79.54022989 + 16.27705113

Reorder the terms:
16.27705113 + -8.068965517x + x2 = 79.54022989 + 16.27705113

Combine like terms: 79.54022989 + 16.27705113 = 95.81728102
16.27705113 + -8.068965517x + x2 = 95.81728102

Factor a perfect square on the left side:
(x + -4.034482759)(x + -4.034482759) = 95.81728102

Calculate the square root of the right side: 9.788630191

Break this problem into two subproblems by setting 
(x + -4.034482759) equal to 9.788630191 and -9.788630191.

Subproblem 1
x + -4.034482759 = 9.788630191

Simplifying
x + -4.034482759 = 9.788630191

Reorder the terms:
-4.034482759 + x = 9.788630191

Solving
-4.034482759 + x = 9.788630191

Solving for variable 'x'.

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

Add '4.034482759' to each side of the equation.
-4.034482759 + 4.034482759 + x = 9.788630191 + 4.034482759

Combine like terms: -4.034482759 + 4.034482759 = 0.000000000
0.000000000 + x = 9.788630191 + 4.034482759
x = 9.788630191 + 4.034482759

Combine like terms: 9.788630191 + 4.034482759 = 13.82311295
x = 13.82311295

Simplifying
x = 13.82311295

Subproblem 2
x + -4.034482759 = -9.788630191

Simplifying
x + -4.034482759 = -9.788630191

Reorder the terms:
-4.034482759 + x = -9.788630191

Solving
-4.034482759 + x = -9.788630191

Solving for variable 'x'.

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

Add '4.034482759' to each side of the equation.
-4.034482759 + 4.034482759 + x = -9.788630191 + 4.034482759

Combine like terms: -4.034482759 + 4.034482759 = 0.000000000
0.000000000 + x = -9.788630191 + 4.034482759
x = -9.788630191 + 4.034482759

Combine like terms: -9.788630191 + 4.034482759 = -5.754147432
x = -5.754147432

Simplifying
x = -5.754147432

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.82311295, -5.754147432}