(x-6)(x-7)=2

Solution for (x-6)(x-7)=2 equation:

Simplifying
(x + -6)(x + -7) = 2

Reorder the terms:
(-6 + x)(x + -7) = 2

Reorder the terms:
(-6 + x)(-7 + x) = 2

Multiply (-6 + x) * (-7 + x)
(-6(-7 + x) + x(-7 + x)) = 2
((-7 * -6 + x * -6) + x(-7 + x)) = 2
((42 + -6x) + x(-7 + x)) = 2
(42 + -6x + (-7 * x + x * x)) = 2
(42 + -6x + (-7x + x2)) = 2

Combine like terms: -6x + -7x = -13x
(42 + -13x + x2) = 2

Solving
42 + -13x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
42 + -2 + -13x + x2 = 2 + -2

Combine like terms: 42 + -2 = 40
40 + -13x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
40 + -13x + x2 = 0

Factor a trinomial.
(5 + -1x)(8 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {5, 8}