(x-6)(x-2)=5

Solution for (x-6)(x-2)=5 equation:

Simplifying
(x + -6)(x + -2) = 5

Reorder the terms:
(-6 + x)(x + -2) = 5

Reorder the terms:
(-6 + x)(-2 + x) = 5

Multiply (-6 + x) * (-2 + x)
(-6(-2 + x) + x(-2 + x)) = 5
((-2 * -6 + x * -6) + x(-2 + x)) = 5
((12 + -6x) + x(-2 + x)) = 5
(12 + -6x + (-2 * x + x * x)) = 5
(12 + -6x + (-2x + x2)) = 5

Combine like terms: -6x + -2x = -8x
(12 + -8x + x2) = 5

Solving
12 + -8x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
12 + -5 + -8x + x2 = 5 + -5

Combine like terms: 12 + -5 = 7
7 + -8x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
7 + -8x + x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}