3(x-5)(6-2x)=0

Solution for 3(x-5)(6-2x)=0 equation:

Simplifying
3(x + -5)(6 + -2x) = 0

Reorder the terms:
3(-5 + x)(6 + -2x) = 0

Multiply (-5 + x) * (6 + -2x)
3(-5(6 + -2x) + x(6 + -2x)) = 0
3((6 * -5 + -2x * -5) + x(6 + -2x)) = 0
3((-30 + 10x) + x(6 + -2x)) = 0
3(-30 + 10x + (6 * x + -2x * x)) = 0
3(-30 + 10x + (6x + -2x2)) = 0

Combine like terms: 10x + 6x = 16x
3(-30 + 16x + -2x2) = 0
(-30 * 3 + 16x * 3 + -2x2 * 3) = 0
(-90 + 48x + -6x2) = 0

Solving
-90 + 48x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 8x + -1x2) = 0

Factor a trinomial.
6((-5 + x)(3 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {5, 3}