2x-6=-2x(x-9)

Solution for 2x-6=-2x(x-9) equation:

Simplifying
2x + -6 = -2x(x + -9)

Reorder the terms:
-6 + 2x = -2x(x + -9)

Reorder the terms:
-6 + 2x = -2x(-9 + x)
-6 + 2x = (-9 * -2x + x * -2x)
-6 + 2x = (18x + -2x2)

Solving
-6 + 2x = 18x + -2x2

Solving for variable 'x'.

Combine like terms: 2x + -18x = -16x
-6 + -16x + 2x2 = 18x + -2x2 + -18x + 2x2

Reorder the terms:
-6 + -16x + 2x2 = 18x + -18x + -2x2 + 2x2

Combine like terms: 18x + -18x = 0
-6 + -16x + 2x2 = 0 + -2x2 + 2x2
-6 + -16x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-6 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -8x + x2 = 0

Solving
-3 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -8x + x2 = 0 + 3

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

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

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 3 + 16

Reorder the terms:
16 + -8x + x2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8x + x2 = 19

Factor a perfect square on the left side:
(x + -4)(x + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1
x + -4 = 4.358898944

Simplifying
x + -4 = 4.358898944

Reorder the terms:
-4 + x = 4.358898944

Solving
-4 + x = 4.358898944

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.358898944 + 4
x = 4.358898944 + 4

Combine like terms: 4.358898944 + 4 = 8.358898944
x = 8.358898944

Simplifying
x = 8.358898944

Subproblem 2
x + -4 = -4.358898944

Simplifying
x + -4 = -4.358898944

Reorder the terms:
-4 + x = -4.358898944

Solving
-4 + x = -4.358898944

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.358898944 + 4
x = -4.358898944 + 4

Combine like terms: -4.358898944 + 4 = -0.358898944
x = -0.358898944

Simplifying
x = -0.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.358898944, -0.358898944}
Solution
x = {8.358898944, -0.358898944}