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

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

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

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

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

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

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

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

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

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

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

Multiply (-3 + x) * (2 + x)
-2 + 1x + x2 = (-3(2 + x) + x(2 + x))
-2 + 1x + x2 = ((2 * -3 + x * -3) + x(2 + x))
-2 + 1x + x2 = ((-6 + -3x) + x(2 + x))
-2 + 1x + x2 = (-6 + -3x + (2 * x + x * x))
-2 + 1x + x2 = (-6 + -3x + (2x + x2))

Combine like terms: -3x + 2x = -1x
-2 + 1x + x2 = (-6 + -1x + x2)

Add '-1x2' to each side of the equation.
-2 + 1x + x2 + -1x2 = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x + 0 = -6 + -1x + x2 + -1x2
-2 + 1x = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x = -6 + -1x + 0
-2 + 1x = -6 + -1x

Solving
-2 + 1x = -6 + -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.
-2 + 1x + x = -6 + -1x + x

Combine like terms: 1x + x = 2x
-2 + 2x = -6 + -1x + x

Combine like terms: -1x + x = 0
-2 + 2x = -6 + 0
-2 + 2x = -6

Add '2' to each side of the equation.
-2 + 2 + 2x = -6 + 2

Combine like terms: -2 + 2 = 0
0 + 2x = -6 + 2
2x = -6 + 2

Combine like terms: -6 + 2 = -4
2x = -4

Divide each side by '2'.
x = -2

Simplifying
x = -2