(x-10)(3x-6)=0

Solution for (x-10)(3x-6)=0 equation:

Simplifying
(x + -10)(3x + -6) = 0

Reorder the terms:
(-10 + x)(3x + -6) = 0

Reorder the terms:
(-10 + x)(-6 + 3x) = 0

Multiply (-10 + x) * (-6 + 3x)
(-10(-6 + 3x) + x(-6 + 3x)) = 0
((-6 * -10 + 3x * -10) + x(-6 + 3x)) = 0
((60 + -30x) + x(-6 + 3x)) = 0
(60 + -30x + (-6 * x + 3x * x)) = 0
(60 + -30x + (-6x + 3x2)) = 0

Combine like terms: -30x + -6x = -36x
(60 + -36x + 3x2) = 0

Solving
60 + -36x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -12x + x2) = 0

Factor a trinomial.
3((2 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {2, 10}