x^2-x=4ax

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

Simplifying
x2 + -1x = 4ax

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

Solving
-1x + x2 = 4ax

Solving for variable 'x'.

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

Combine like terms: 4ax + -4ax = 0
-4ax + -1x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4a + -1 + x) = 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 '(-4a + -1 + x)' equal to zero and attempt to solve:

Simplifying
-4a + -1 + x = 0

Reorder the terms:
-1 + -4a + x = 0

Solving
-1 + -4a + x = 0

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

Add '1' to each side of the equation.
-1 + -4a + 1 + x = 0 + 1

Reorder the terms:
-1 + 1 + -4a + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4a + x = 0 + 1
-4a + x = 0 + 1

Combine like terms: 0 + 1 = 1
-4a + x = 1

Add '4a' to each side of the equation.
-4a + 4a + x = 1 + 4a

Combine like terms: -4a + 4a = 0
0 + x = 1 + 4a
x = 1 + 4a

Simplifying
x = 1 + 4a
Solution
x = {0, 1 + 4a}