x^2=x+2ax

Solution for x^2=x+2ax equation:

Simplifying
x2 = x + 2ax

Reorder the terms:
x2 = 2ax + x

Solving
x2 = 2ax + x

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2a + -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 '(-2a + -1 + x)' equal to zero and attempt to solve:

Simplifying
-2a + -1 + x = 0

Reorder the terms:
-1 + -2a + x = 0

Solving
-1 + -2a + 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 + -2a + 1 + x = 0 + 1

Reorder the terms:
-1 + 1 + -2a + x = 0 + 1

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

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

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

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

Simplifying
x = 1 + 2a
Solution
x = {0, 1 + 2a}