-x^2+4x=x

Solution for -x^2+4x=x equation:

Simplifying
-1x2 + 4x = x

Reorder the terms:
4x + -1x2 = x

Solving
4x + -1x2 = x

Solving for variable 'x'.

Reorder the terms:
4x + -1x + -1x2 = x + -1x

Combine like terms: 4x + -1x = 3x
3x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
3x + -1x2 = 0

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}