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

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

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

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

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

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

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.