x(1-2x)=x-8

Solution for x(1-2x)=x-8 equation:

Simplifying
x(1 + -2x) = x + -8
(1 * x + -2x * x) = x + -8
(1x + -2x2) = x + -8

Reorder the terms:
1x + -2x2 = -8 + x

Solving
1x + -2x2 = -8 + x

Solving for variable 'x'.

Reorder the terms:
8 + 1x + -1x + -2x2 = -8 + x + 8 + -1x

Combine like terms: 1x + -1x = 0
8 + 0 + -2x2 = -8 + x + 8 + -1x
8 + -2x2 = -8 + x + 8 + -1x

Reorder the terms:
8 + -2x2 = -8 + 8 + x + -1x

Combine like terms: -8 + 8 = 0
8 + -2x2 = 0 + x + -1x
8 + -2x2 = x + -1x

Combine like terms: x + -1x = 0
8 + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -1x2) = 0

Factor a difference between two squares.
2((2 + x)(2 + -1x)) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}