3(x-6)(2.9x-6)=600

Solution for 3(x-6)(2.9x-6)=600 equation:

Simplifying
3(x + -6)(2.9x + -6) = 600

Reorder the terms:
3(-6 + x)(2.9x + -6) = 600

Reorder the terms:
3(-6 + x)(-6 + 2.9x) = 600

Multiply (-6 + x) * (-6 + 2.9x)
3(-6(-6 + 2.9x) + x(-6 + 2.9x)) = 600
3((-6 * -6 + 2.9x * -6) + x(-6 + 2.9x)) = 600
3((36 + -17.4x) + x(-6 + 2.9x)) = 600
3(36 + -17.4x + (-6 * x + 2.9x * x)) = 600
3(36 + -17.4x + (-6x + 2.9x2)) = 600

Combine like terms: -17.4x + -6x = -23.4x
3(36 + -23.4x + 2.9x2) = 600
(36 * 3 + -23.4x * 3 + 2.9x2 * 3) = 600
(108 + -70.2x + 8.7x2) = 600

Solving
108 + -70.2x + 8.7x2 = 600

Solving for variable 'x'.

Reorder the terms:
108 + -600 + -70.2x + 8.7x2 = 600 + -600

Combine like terms: 108 + -600 = -492
-492 + -70.2x + 8.7x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-492 + -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'.
-56.55172414 + -8.068965517x + x2 = 0

Move the constant term to the right:

Add '56.55172414' to each side of the equation.
-56.55172414 + -8.068965517x + 56.55172414 + x2 = 0 + 56.55172414

Reorder the terms:
-56.55172414 + 56.55172414 + -8.068965517x + x2 = 0 + 56.55172414

Combine like terms: -56.55172414 + 56.55172414 = 0.00000000
0.00000000 + -8.068965517x + x2 = 0 + 56.55172414
-8.068965517x + x2 = 0 + 56.55172414

Combine like terms: 0 + 56.55172414 = 56.55172414
-8.068965517x + x2 = 56.55172414

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 = 56.55172414 + 16.27705113

Reorder the terms:
16.27705113 + -8.068965517x + x2 = 56.55172414 + 16.27705113

Combine like terms: 56.55172414 + 16.27705113 = 72.82877527
16.27705113 + -8.068965517x + x2 = 72.82877527

Factor a perfect square on the left side:
(x + -4.034482759)(x + -4.034482759) = 72.82877527

Calculate the square root of the right side: 8.533977693

Break this problem into two subproblems by setting 
(x + -4.034482759) equal to 8.533977693 and -8.533977693.

Subproblem 1
x + -4.034482759 = 8.533977693

Simplifying
x + -4.034482759 = 8.533977693

Reorder the terms:
-4.034482759 + x = 8.533977693

Solving
-4.034482759 + x = 8.533977693

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 = 8.533977693 + 4.034482759

Combine like terms: -4.034482759 + 4.034482759 = 0.000000000
0.000000000 + x = 8.533977693 + 4.034482759
x = 8.533977693 + 4.034482759

Combine like terms: 8.533977693 + 4.034482759 = 12.568460452
x = 12.568460452

Simplifying
x = 12.568460452

Subproblem 2
x + -4.034482759 = -8.533977693

Simplifying
x + -4.034482759 = -8.533977693

Reorder the terms:
-4.034482759 + x = -8.533977693

Solving
-4.034482759 + x = -8.533977693

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 = -8.533977693 + 4.034482759

Combine like terms: -4.034482759 + 4.034482759 = 0.000000000
0.000000000 + x = -8.533977693 + 4.034482759
x = -8.533977693 + 4.034482759

Combine like terms: -8.533977693 + 4.034482759 = -4.499494934
x = -4.499494934

Simplifying
x = -4.499494934

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.568460452, -4.499494934}