2(2x-1)(x)=3(x)(x)+x(x-1)

Solution for 2(2x-1)(x)=3(x)(x)+x(x-1) equation:

Simplifying
2(2x + -1)(x) = 3(x)(x) + x(x + -1)

Reorder the terms:
2(-1 + 2x)(x) = 3(x)(x) + x(x + -1)

Reorder the terms for easier multiplication:
2x(-1 + 2x) = 3(x)(x) + x(x + -1)
(-1 * 2x + 2x * 2x) = 3(x)(x) + x(x + -1)
(-2x + 4x2) = 3(x)(x) + x(x + -1)

Multiply x * x
-2x + 4x2 = 3x2 + x(x + -1)

Reorder the terms:
-2x + 4x2 = 3x2 + x(-1 + x)
-2x + 4x2 = 3x2 + (-1 * x + x * x)
-2x + 4x2 = 3x2 + (-1x + x2)

Reorder the terms:
-2x + 4x2 = -1x + 3x2 + x2

Combine like terms: 3x2 + x2 = 4x2
-2x + 4x2 = -1x + 4x2

Add '-4x2' to each side of the equation.
-2x + 4x2 + -4x2 = -1x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2x + 0 = -1x + 4x2 + -4x2
-2x = -1x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2x = -1x + 0
-2x = -1x

Solving
-2x = -1x

Solving for variable 'x'.

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

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

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

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

Divide each side by '-1'.
x = 0

Simplifying
x = 0