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

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

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

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

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

Multiply (-1 + 2x) * (1 + x)
2x2 = (-1(1 + x) + 2x * (1 + x))
2x2 = ((1 * -1 + x * -1) + 2x * (1 + x))
2x2 = ((-1 + -1x) + 2x * (1 + x))
2x2 = (-1 + -1x + (1 * 2x + x * 2x))
2x2 = (-1 + -1x + (2x + 2x2))

Combine like terms: -1x + 2x = 1x
2x2 = (-1 + 1x + 2x2)

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

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

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

Solving
0 = -1 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
0 + -1x = -1 + 1x + -1x
Remove the zero:
-1x = -1 + 1x + -1x

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

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

Simplifying
x = 1