6x*(50-x)*4=170

Solution for 6x*(50-x)*4=170 equation:

Simplifying
6x(50 + -1x) * 4 = 170

Reorder the terms for easier multiplication:
6 * 4x(50 + -1x) = 170

Multiply 6 * 4
24x(50 + -1x) = 170
(50 * 24x + -1x * 24x) = 170
(1200x + -24x2) = 170

Solving
1200x + -24x2 = 170

Solving for variable 'x'.

Reorder the terms:
-170 + 1200x + -24x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-170 + 1200x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-85 + 600x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-85 + 600x + -12x2)' equal to zero and attempt to solve:

Simplifying
-85 + 600x + -12x2 = 0

Solving
-85 + 600x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
7.083333333 + -50x + x2 = 0

Move the constant term to the right:

Add '-7.083333333' to each side of the equation.
7.083333333 + -50x + -7.083333333 + x2 = 0 + -7.083333333

Reorder the terms:
7.083333333 + -7.083333333 + -50x + x2 = 0 + -7.083333333

Combine like terms: 7.083333333 + -7.083333333 = 0.000000000
0.000000000 + -50x + x2 = 0 + -7.083333333
-50x + x2 = 0 + -7.083333333

Combine like terms: 0 + -7.083333333 = -7.083333333
-50x + x2 = -7.083333333

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -7.083333333 + 625

Reorder the terms:
625 + -50x + x2 = -7.083333333 + 625

Combine like terms: -7.083333333 + 625 = 617.916666667
625 + -50x + x2 = 617.916666667

Factor a perfect square on the left side:
(x + -25)(x + -25) = 617.916666667

Calculate the square root of the right side: 24.857929654

Break this problem into two subproblems by setting 
(x + -25) equal to 24.857929654 and -24.857929654.

Subproblem 1
x + -25 = 24.857929654

Simplifying
x + -25 = 24.857929654

Reorder the terms:
-25 + x = 24.857929654

Solving
-25 + x = 24.857929654

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 24.857929654 + 25

Combine like terms: -25 + 25 = 0
0 + x = 24.857929654 + 25
x = 24.857929654 + 25

Combine like terms: 24.857929654 + 25 = 49.857929654
x = 49.857929654

Simplifying
x = 49.857929654

Subproblem 2
x + -25 = -24.857929654

Simplifying
x + -25 = -24.857929654

Reorder the terms:
-25 + x = -24.857929654

Solving
-25 + x = -24.857929654

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -24.857929654 + 25

Combine like terms: -25 + 25 = 0
0 + x = -24.857929654 + 25
x = -24.857929654 + 25

Combine like terms: -24.857929654 + 25 = 0.142070346
x = 0.142070346

Simplifying
x = 0.142070346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {49.857929654, 0.142070346}
Solution
x = {49.857929654, 0.142070346}