(X-5)(X-6)=56

Solution for (X-5)(X-6)=56 equation:

Simplifying
(X + -5)(X + -6) = 56

Reorder the terms:
(-5 + X)(X + -6) = 56

Reorder the terms:
(-5 + X)(-6 + X) = 56

Multiply (-5 + X) * (-6 + X)
(-5(-6 + X) + X(-6 + X)) = 56
((-6 * -5 + X * -5) + X(-6 + X)) = 56
((30 + -5X) + X(-6 + X)) = 56
(30 + -5X + (-6 * X + X * X)) = 56
(30 + -5X + (-6X + X2)) = 56

Combine like terms: -5X + -6X = -11X
(30 + -11X + X2) = 56

Solving
30 + -11X + X2 = 56

Solving for variable 'X'.

Reorder the terms:
30 + -56 + -11X + X2 = 56 + -56

Combine like terms: 30 + -56 = -26
-26 + -11X + X2 = 56 + -56

Combine like terms: 56 + -56 = 0
-26 + -11X + X2 = 0

Factor a trinomial.
(-2 + -1X)(13 + -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 '(13 + -1X)' equal to zero and attempt to solve:

Simplifying
13 + -1X = 0

Solving
13 + -1X = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1X = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1X = 0 + -13
-1X = 0 + -13

Combine like terms: 0 + -13 = -13
-1X = -13

Divide each side by '-1'.
X = 13

Simplifying
X = 13
Solution
X = {-2, 13}