21k^2+3k=0

Solution for 21k^2+3k=0 equation:

Simplifying
21k2 + 3k = 0

Reorder the terms:
3k + 21k2 = 0

Solving
3k + 21k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3k'.
3k(1 + 7k) = 0

Ignore the factor 3.
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 '(1 + 7k)' equal to zero and attempt to solve:

Simplifying
1 + 7k = 0

Solving
1 + 7k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7k = 0 + -1
7k = 0 + -1

Combine like terms: 0 + -1 = -1
7k = -1

Divide each side by '7'.
k = -0.1428571429

Simplifying
k = -0.1428571429
Solution
k = {0, -0.1428571429}