2(86-x)(5x)=330

Solution for 2(86-x)(5x)=330 equation:

Simplifying
2(86 + -1x)(5x) = 330

Remove parenthesis around (5x)
2(86 + -1x) * 5x = 330

Reorder the terms for easier multiplication:
2 * 5x(86 + -1x) = 330

Multiply 2 * 5
10x(86 + -1x) = 330
(86 * 10x + -1x * 10x) = 330
(860x + -10x2) = 330

Solving
860x + -10x2 = 330

Solving for variable 'x'.

Reorder the terms:
-330 + 860x + -10x2 = 330 + -330

Combine like terms: 330 + -330 = 0
-330 + 860x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-33 + 86x + -1x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-33 + 86x + -1x2)' equal to zero and attempt to solve:

Simplifying
-33 + 86x + -1x2 = 0

Solving
-33 + 86x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
33 + -86x + x2 = 0

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -86x + -33 + x2 = 0 + -33

Reorder the terms:
33 + -33 + -86x + x2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -86x + x2 = 0 + -33
-86x + x2 = 0 + -33

Combine like terms: 0 + -33 = -33
-86x + x2 = -33

The x term is -86x.  Take half its coefficient (-43).
Square it (1849) and add it to both sides.

Add '1849' to each side of the equation.
-86x + 1849 + x2 = -33 + 1849

Reorder the terms:
1849 + -86x + x2 = -33 + 1849

Combine like terms: -33 + 1849 = 1816
1849 + -86x + x2 = 1816

Factor a perfect square on the left side:
(x + -43)(x + -43) = 1816

Calculate the square root of the right side: 42.614551505

Break this problem into two subproblems by setting 
(x + -43) equal to 42.614551505 and -42.614551505.

Subproblem 1
x + -43 = 42.614551505

Simplifying
x + -43 = 42.614551505

Reorder the terms:
-43 + x = 42.614551505

Solving
-43 + x = 42.614551505

Solving for variable 'x'.

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

Add '43' to each side of the equation.
-43 + 43 + x = 42.614551505 + 43

Combine like terms: -43 + 43 = 0
0 + x = 42.614551505 + 43
x = 42.614551505 + 43

Combine like terms: 42.614551505 + 43 = 85.614551505
x = 85.614551505

Simplifying
x = 85.614551505

Subproblem 2
x + -43 = -42.614551505

Simplifying
x + -43 = -42.614551505

Reorder the terms:
-43 + x = -42.614551505

Solving
-43 + x = -42.614551505

Solving for variable 'x'.

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

Add '43' to each side of the equation.
-43 + 43 + x = -42.614551505 + 43

Combine like terms: -43 + 43 = 0
0 + x = -42.614551505 + 43
x = -42.614551505 + 43

Combine like terms: -42.614551505 + 43 = 0.385448495
x = 0.385448495

Simplifying
x = 0.385448495

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {85.614551505, 0.385448495}
Solution
x = {85.614551505, 0.385448495}