x^2-3x+2x-6=(x-2)(x+3)

Solution for x^2-3x+2x-6=(x-2)(x+3) equation:

Simplifying
x2 + -3x + 2x + -6 = (x + -2)(x + 3)

Reorder the terms:
-6 + -3x + 2x + x2 = (x + -2)(x + 3)

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

Reorder the terms:
-6 + -1x + x2 = (-2 + x)(x + 3)

Reorder the terms:
-6 + -1x + x2 = (-2 + x)(3 + x)

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

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

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

Reorder the terms:
-6 + 6 + -1x + x2 = -6 + 1x + 6 + x2

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

Reorder the terms:
-1x + x2 = -6 + 6 + 1x + x2

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

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

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

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

Solving
-1x = 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.
-1x + -1x = 1x + -1x

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

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

Divide each side by '-2'.
x = 0

Simplifying
x = 0