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

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

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

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

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

Multiply (-5 + x) * (-6 + x)
(-5(-6 + x) + x(-6 + x)) = 2
((-6 * -5 + x * -5) + x(-6 + x)) = 2
((30 + -5x) + x(-6 + x)) = 2
(30 + -5x + (-6 * x + x * x)) = 2
(30 + -5x + (-6x + x2)) = 2

Combine like terms: -5x + -6x = -11x
(30 + -11x + x2) = 2

Solving
30 + -11x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
30 + -2 + -11x + x2 = 2 + -2

Combine like terms: 30 + -2 = 28
28 + -11x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
28 + -11x + x2 = 0

Factor a trinomial.
(4 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
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 = {4, 7}