2x^2-x=x(-1+x)+1

Solution for 2x^2-x=x(-1+x)+1 equation:

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

Reorder the terms:
-1x + 2x2 = x(-1 + x) + 1
-1x + 2x2 = (-1 * x + x * x) + 1
-1x + 2x2 = (-1x + x2) + 1

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

Add 'x' to each side of the equation.
-1x + x + 2x2 = 1 + -1x + x + x2

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

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

Solving
2x2 = 1 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
2x2 + -1x2 = 1 + x2 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
1x2 = 1 + x2 + -1x2

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

Divide each side by '1'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}