(x-4)(x-8)=5

Solution for (x-4)(x-8)=5 equation:

Simplifying
(x + -4)(x + -8) = 5

Reorder the terms:
(-4 + x)(x + -8) = 5

Reorder the terms:
(-4 + x)(-8 + x) = 5

Multiply (-4 + x) * (-8 + x)
(-4(-8 + x) + x(-8 + x)) = 5
((-8 * -4 + x * -4) + x(-8 + x)) = 5
((32 + -4x) + x(-8 + x)) = 5
(32 + -4x + (-8 * x + x * x)) = 5
(32 + -4x + (-8x + x2)) = 5

Combine like terms: -4x + -8x = -12x
(32 + -12x + x2) = 5

Solving
32 + -12x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
32 + -5 + -12x + x2 = 5 + -5

Combine like terms: 32 + -5 = 27
27 + -12x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
27 + -12x + x2 = 0

Factor a trinomial.
(3 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}