-2x(x-2)-4x=3(x+1)+9x

Solution for -2x(x-2)-4x=3(x+1)+9x equation:

Simplifying
-2x(x + -2) + -4x = 3(x + 1) + 9x

Reorder the terms:
-2x(-2 + x) + -4x = 3(x + 1) + 9x
(-2 * -2x + x * -2x) + -4x = 3(x + 1) + 9x
(4x + -2x2) + -4x = 3(x + 1) + 9x

Reorder the terms:
4x + -4x + -2x2 = 3(x + 1) + 9x

Combine like terms: 4x + -4x = 0
0 + -2x2 = 3(x + 1) + 9x
-2x2 = 3(x + 1) + 9x

Reorder the terms:
-2x2 = 3(1 + x) + 9x
-2x2 = (1 * 3 + x * 3) + 9x
-2x2 = (3 + 3x) + 9x

Combine like terms: 3x + 9x = 12x
-2x2 = 3 + 12x

Solving
-2x2 = 3 + 12x

Solving for variable 'x'.

Reorder the terms:
-3 + -12x + -2x2 = 3 + 12x + -3 + -12x

Reorder the terms:
-3 + -12x + -2x2 = 3 + -3 + 12x + -12x

Combine like terms: 3 + -3 = 0
-3 + -12x + -2x2 = 0 + 12x + -12x
-3 + -12x + -2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-3 + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 12x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 12x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 12x + 2x2 = 0

Solving
3 + 12x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 6x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 6x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 6x + x2 = 0 + -1.5
6x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
6x + x2 = -1.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -1.5 + 9

Reorder the terms:
9 + 6x + x2 = -1.5 + 9

Combine like terms: -1.5 + 9 = 7.5
9 + 6x + x2 = 7.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(x + 3) equal to 2.738612788 and -2.738612788.

Subproblem 1
x + 3 = 2.738612788

Simplifying
x + 3 = 2.738612788

Reorder the terms:
3 + x = 2.738612788

Solving
3 + x = 2.738612788

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.738612788 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.738612788 + -3
x = 2.738612788 + -3

Combine like terms: 2.738612788 + -3 = -0.261387212
x = -0.261387212

Simplifying
x = -0.261387212

Subproblem 2
x + 3 = -2.738612788

Simplifying
x + 3 = -2.738612788

Reorder the terms:
3 + x = -2.738612788

Solving
3 + x = -2.738612788

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.738612788 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.738612788 + -3
x = -2.738612788 + -3

Combine like terms: -2.738612788 + -3 = -5.738612788
x = -5.738612788

Simplifying
x = -5.738612788

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.261387212, -5.738612788}
Solution
x = {-0.261387212, -5.738612788}