(x-2)(x-4)=3

Solution for (x-2)(x-4)=3 equation:

Simplifying
(x + -2)(x + -4) = 3

Reorder the terms:
(-2 + x)(x + -4) = 3

Reorder the terms:
(-2 + x)(-4 + x) = 3

Multiply (-2 + x) * (-4 + x)
(-2(-4 + x) + x(-4 + x)) = 3
((-4 * -2 + x * -2) + x(-4 + x)) = 3
((8 + -2x) + x(-4 + x)) = 3
(8 + -2x + (-4 * x + x * x)) = 3
(8 + -2x + (-4x + x2)) = 3

Combine like terms: -2x + -4x = -6x
(8 + -6x + x2) = 3

Solving
8 + -6x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
8 + -3 + -6x + x2 = 3 + -3

Combine like terms: 8 + -3 = 5
5 + -6x + x2 = 3 + -3

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

Factor a trinomial.
(1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}