(x-5)(x-12)-44=0

Solution for (x-5)(x-12)-44=0 equation:

Simplifying
(x + -5)(x + -12) + -44 = 0

Reorder the terms:
(-5 + x)(x + -12) + -44 = 0

Reorder the terms:
(-5 + x)(-12 + x) + -44 = 0

Multiply (-5 + x) * (-12 + x)
(-5(-12 + x) + x(-12 + x)) + -44 = 0
((-12 * -5 + x * -5) + x(-12 + x)) + -44 = 0
((60 + -5x) + x(-12 + x)) + -44 = 0
(60 + -5x + (-12 * x + x * x)) + -44 = 0
(60 + -5x + (-12x + x2)) + -44 = 0

Combine like terms: -5x + -12x = -17x
(60 + -17x + x2) + -44 = 0

Reorder the terms:
60 + -44 + -17x + x2 = 0

Combine like terms: 60 + -44 = 16
16 + -17x + x2 = 0

Solving
16 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(16 + -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 '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {1, 16}