(x-3)(x-5)=3

Solution for (x-3)(x-5)=3 equation:

Simplifying
(x + -3)(x + -5) = 3

Reorder the terms:
(-3 + x)(x + -5) = 3

Reorder the terms:
(-3 + x)(-5 + x) = 3

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x)) = 3
((-5 * -3 + x * -3) + x(-5 + x)) = 3
((15 + -3x) + x(-5 + x)) = 3
(15 + -3x + (-5 * x + x * x)) = 3
(15 + -3x + (-5x + x2)) = 3

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2) = 3

Solving
15 + -8x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
15 + -3 + -8x + x2 = 3 + -3

Combine like terms: 15 + -3 = 12
12 + -8x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
12 + -8x + x2 = 0

Factor a trinomial.
(2 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {2, 6}