20x-4x*x-12x=8x*x-23x-3

Solution for 20x-4x*x-12x=8x*x-23x-3 equation:

Simplifying
20x + -4x * x + -12x = 8x * x + -23x + -3

Multiply x * x
20x + -4x2 + -12x = 8x * x + -23x + -3

Reorder the terms:
20x + -12x + -4x2 = 8x * x + -23x + -3

Combine like terms: 20x + -12x = 8x
8x + -4x2 = 8x * x + -23x + -3

Multiply x * x
8x + -4x2 = 8x2 + -23x + -3

Reorder the terms:
8x + -4x2 = -3 + -23x + 8x2

Solving
8x + -4x2 = -3 + -23x + 8x2

Solving for variable 'x'.

Reorder the terms:
3 + 8x + 23x + -4x2 + -8x2 = -3 + -23x + 8x2 + 3 + 23x + -8x2

Combine like terms: 8x + 23x = 31x
3 + 31x + -4x2 + -8x2 = -3 + -23x + 8x2 + 3 + 23x + -8x2

Combine like terms: -4x2 + -8x2 = -12x2
3 + 31x + -12x2 = -3 + -23x + 8x2 + 3 + 23x + -8x2

Reorder the terms:
3 + 31x + -12x2 = -3 + 3 + -23x + 23x + 8x2 + -8x2

Combine like terms: -3 + 3 = 0
3 + 31x + -12x2 = 0 + -23x + 23x + 8x2 + -8x2
3 + 31x + -12x2 = -23x + 23x + 8x2 + -8x2

Combine like terms: -23x + 23x = 0
3 + 31x + -12x2 = 0 + 8x2 + -8x2
3 + 31x + -12x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
3 + 31x + -12x2 = 0

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

Divide each side by '-12'.
-0.25 + -2.583333333x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.583333333x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.583333333x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.583333333x + x2 = 0 + 0.25
-2.583333333x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.583333333x + x2 = 0.25

The x term is -2.583333333x.  Take half its coefficient (-1.291666667).
Square it (1.668402779) and add it to both sides.

Add '1.668402779' to each side of the equation.
-2.583333333x + 1.668402779 + x2 = 0.25 + 1.668402779

Reorder the terms:
1.668402779 + -2.583333333x + x2 = 0.25 + 1.668402779

Combine like terms: 0.25 + 1.668402779 = 1.918402779
1.668402779 + -2.583333333x + x2 = 1.918402779

Factor a perfect square on the left side:
(x + -1.291666667)(x + -1.291666667) = 1.918402779

Calculate the square root of the right side: 1.385064179

Break this problem into two subproblems by setting 
(x + -1.291666667) equal to 1.385064179 and -1.385064179.

Subproblem 1
x + -1.291666667 = 1.385064179

Simplifying
x + -1.291666667 = 1.385064179

Reorder the terms:
-1.291666667 + x = 1.385064179

Solving
-1.291666667 + x = 1.385064179

Solving for variable 'x'.

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

Add '1.291666667' to each side of the equation.
-1.291666667 + 1.291666667 + x = 1.385064179 + 1.291666667

Combine like terms: -1.291666667 + 1.291666667 = 0.000000000
0.000000000 + x = 1.385064179 + 1.291666667
x = 1.385064179 + 1.291666667

Combine like terms: 1.385064179 + 1.291666667 = 2.676730846
x = 2.676730846

Simplifying
x = 2.676730846

Subproblem 2
x + -1.291666667 = -1.385064179

Simplifying
x + -1.291666667 = -1.385064179

Reorder the terms:
-1.291666667 + x = -1.385064179

Solving
-1.291666667 + x = -1.385064179

Solving for variable 'x'.

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

Add '1.291666667' to each side of the equation.
-1.291666667 + 1.291666667 + x = -1.385064179 + 1.291666667

Combine like terms: -1.291666667 + 1.291666667 = 0.000000000
0.000000000 + x = -1.385064179 + 1.291666667
x = -1.385064179 + 1.291666667

Combine like terms: -1.385064179 + 1.291666667 = -0.093397512
x = -0.093397512

Simplifying
x = -0.093397512

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.676730846, -0.093397512}