(k-3k)(k-10)=0

Solution for (k-3k)(k-10)=0 equation:

Simplifying
(k + -3k)(k + -10) = 0

Combine like terms: k + -3k = -2k
(-2k)(k + -10) = 0

Remove parenthesis around (-2k)
-2k(k + -10) = 0

Reorder the terms:
-2k(-10 + k) = 0
(-10 * -2k + k * -2k) = 0
(20k + -2k2) = 0

Solving
20k + -2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2k'.
2k(10 + -1k) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

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

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

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

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

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

Simplifying
k = 10
Solution
k = {0, 10}