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

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

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

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

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

Multiply (-3 + x) * (-2 + x)
(-3(-2 + x) + x(-2 + x)) = 0
((-2 * -3 + x * -3) + x(-2 + x)) = 0
((6 + -3x) + x(-2 + x)) = 0
(6 + -3x + (-2 * x + x * x)) = 0
(6 + -3x + (-2x + x2)) = 0

Combine like terms: -3x + -2x = -5x
(6 + -5x + x2) = 0

Solving
6 + -5x + 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}