(x-5)(3x-6)=0

Solution for (x-5)(3x-6)=0 equation:

Simplifying
(x + -5)(3x + -6) = 0

Reorder the terms:
(-5 + x)(3x + -6) = 0

Reorder the terms:
(-5 + x)(-6 + 3x) = 0

Multiply (-5 + x) * (-6 + 3x)
(-5(-6 + 3x) + x(-6 + 3x)) = 0
((-6 * -5 + 3x * -5) + x(-6 + 3x)) = 0
((30 + -15x) + x(-6 + 3x)) = 0
(30 + -15x + (-6 * x + 3x * x)) = 0
(30 + -15x + (-6x + 3x2)) = 0

Combine like terms: -15x + -6x = -21x
(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}