(x-5)(x-12)=

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

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

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

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

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

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

Solving
60 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {5, 12}