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 = 3x
3x = -1x + x

Combine like terms: -1x + x = 0
3x = 0

Divide each side by '3'.
x = 0

Simplifying
x = 0