3(x-2)(x-5)=0

Solution for 3(x-2)(x-5)=0 equation:

Simplifying
3(x + -2)(x + -5) = 0

Reorder the terms:
3(-2 + x)(x + -5) = 0

Reorder the terms:
3(-2 + x)(-5 + x) = 0

Multiply (-2 + x) * (-5 + x)
3(-2(-5 + x) + x(-5 + x)) = 0
3((-5 * -2 + x * -2) + x(-5 + x)) = 0
3((10 + -2x) + x(-5 + x)) = 0
3(10 + -2x + (-5 * x + x * x)) = 0
3(10 + -2x + (-5x + x2)) = 0

Combine like terms: -2x + -5x = -7x
3(10 + -7x + x2) = 0
(10 * 3 + -7x * 3 + x2 * 3) = 0
(30 + -21x + 3x2) = 0

Solving
30 + -21x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -7x + x2) = 0

Factor a trinomial.
3((2 + -1x)(5 + -1x)) = 0

Ignore the factor 3.
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 '(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 = {2, 5}