3k(k-7)=-36

Solution for 3k(k-7)=-36 equation:

Simplifying
3k(k + -7) = -36

Reorder the terms:
3k(-7 + k) = -36
(-7 * 3k + k * 3k) = -36
(-21k + 3k2) = -36

Solving
-21k + 3k2 = -36

Solving for variable 'k'.

Reorder the terms:
36 + -21k + 3k2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -21k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -7k + k2) = 0

Factor a trinomial.
3((3 + -1k)(4 + -1k)) = 0

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

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

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

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

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

Simplifying
k = 3
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {3, 4}