x(x-3)+2(x-3)=0

Solution for x(x-3)+2(x-3)=0 equation:

Simplifying
x(x + -3) + 2(x + -3) = 0

Reorder the terms:
x(-3 + x) + 2(x + -3) = 0
(-3 * x + x * x) + 2(x + -3) = 0
(-3x + x2) + 2(x + -3) = 0

Reorder the terms:
-3x + x2 + 2(-3 + x) = 0
-3x + x2 + (-3 * 2 + x * 2) = 0
-3x + x2 + (-6 + 2x) = 0

Reorder the terms:
-6 + -3x + 2x + x2 = 0

Combine like terms: -3x + 2x = -1x
-6 + -1x + x2 = 0

Solving
-6 + -1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}