x-6x(x-5)=2x+4(x-20)

Solution for x-6x(x-5)=2x+4(x-20) equation:

Simplifying
x + -6x(x + -5) = 2x + 4(x + -20)

Reorder the terms:
x + -6x(-5 + x) = 2x + 4(x + -20)
x + (-5 * -6x + x * -6x) = 2x + 4(x + -20)
x + (30x + -6x2) = 2x + 4(x + -20)

Combine like terms: x + 30x = 31x
31x + -6x2 = 2x + 4(x + -20)

Reorder the terms:
31x + -6x2 = 2x + 4(-20 + x)
31x + -6x2 = 2x + (-20 * 4 + x * 4)
31x + -6x2 = 2x + (-80 + 4x)

Reorder the terms:
31x + -6x2 = -80 + 2x + 4x

Combine like terms: 2x + 4x = 6x
31x + -6x2 = -80 + 6x

Solving
31x + -6x2 = -80 + 6x

Solving for variable 'x'.

Reorder the terms:
80 + 31x + -6x + -6x2 = -80 + 6x + 80 + -6x

Combine like terms: 31x + -6x = 25x
80 + 25x + -6x2 = -80 + 6x + 80 + -6x

Reorder the terms:
80 + 25x + -6x2 = -80 + 80 + 6x + -6x

Combine like terms: -80 + 80 = 0
80 + 25x + -6x2 = 0 + 6x + -6x
80 + 25x + -6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
80 + 25x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-13.33333333 + -4.166666667x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -4.166666667x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -4.166666667x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -4.166666667x + x2 = 0 + 13.33333333
-4.166666667x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-4.166666667x + x2 = 13.33333333

The x term is -4.166666667x.  Take half its coefficient (-2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
-4.166666667x + 4.340277781 + x2 = 13.33333333 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667x + x2 = 13.33333333 + 4.340277781

Combine like terms: 13.33333333 + 4.340277781 = 17.673611111
4.340277781 + -4.166666667x + x2 = 17.673611111

Factor a perfect square on the left side:
(x + -2.083333334)(x + -2.083333334) = 17.673611111

Calculate the square root of the right side: 4.203999419

Break this problem into two subproblems by setting 
(x + -2.083333334) equal to 4.203999419 and -4.203999419.

Subproblem 1
x + -2.083333334 = 4.203999419

Simplifying
x + -2.083333334 = 4.203999419

Reorder the terms:
-2.083333334 + x = 4.203999419

Solving
-2.083333334 + x = 4.203999419

Solving for variable 'x'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + x = 4.203999419 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + x = 4.203999419 + 2.083333334
x = 4.203999419 + 2.083333334

Combine like terms: 4.203999419 + 2.083333334 = 6.287332753
x = 6.287332753

Simplifying
x = 6.287332753

Subproblem 2
x + -2.083333334 = -4.203999419

Simplifying
x + -2.083333334 = -4.203999419

Reorder the terms:
-2.083333334 + x = -4.203999419

Solving
-2.083333334 + x = -4.203999419

Solving for variable 'x'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + x = -4.203999419 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + x = -4.203999419 + 2.083333334
x = -4.203999419 + 2.083333334

Combine like terms: -4.203999419 + 2.083333334 = -2.120666085
x = -2.120666085

Simplifying
x = -2.120666085

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.287332753, -2.120666085}