(x-5)(3x-12)=0

Solution for (x-5)(3x-12)=0 equation:

Simplifying
(x + -5)(3x + -12) = 0

Reorder the terms:
(-5 + x)(3x + -12) = 0

Reorder the terms:
(-5 + x)(-12 + 3x) = 0

Multiply (-5 + x) * (-12 + 3x)
(-5(-12 + 3x) + x(-12 + 3x)) = 0
((-12 * -5 + 3x * -5) + x(-12 + 3x)) = 0
((60 + -15x) + x(-12 + 3x)) = 0
(60 + -15x + (-12 * x + 3x * x)) = 0
(60 + -15x + (-12x + 3x2)) = 0

Combine like terms: -15x + -12x = -27x
(60 + -27x + 3x2) = 0

Solving
60 + -27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -9x + x2) = 0

Factor a trinomial.
3((4 + -1x)(5 + -1x)) = 0

Ignore the factor 3.
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 '(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
Solution
x = {4, 5}