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

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

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

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

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

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

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

Solving
-6 + 1x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 2}