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

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

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

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

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

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

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

Solving
6 + -5x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
6 + -2 + -5x + x2 = 2 + -2

Combine like terms: 6 + -2 = 4
4 + -5x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
4 + -5x + x2 = 0

Factor a trinomial.
(1 + -1x)(4 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}