3(x-4)(x-5)=0

Solution for 3(x-4)(x-5)=0 equation:

Simplifying
3(x + -4)(x + -5) = 0

Reorder the terms:
3(-4 + x)(x + -5) = 0

Reorder the terms:
3(-4 + x)(-5 + x) = 0

Multiply (-4 + x) * (-5 + x)
3(-4(-5 + x) + x(-5 + x)) = 0
3((-5 * -4 + x * -4) + x(-5 + x)) = 0
3((20 + -4x) + x(-5 + x)) = 0
3(20 + -4x + (-5 * x + x * x)) = 0
3(20 + -4x + (-5x + x2)) = 0

Combine like terms: -4x + -5x = -9x
3(20 + -9x + x2) = 0
(20 * 3 + -9x * 3 + x2 * 3) = 0
(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}