30k-5k^2=45

Solution for 30k-5k^2=45 equation:

Simplifying
30k + -5k2 = 45

Solving
30k + -5k2 = 45

Solving for variable 'k'.

Reorder the terms:
-45 + 30k + -5k2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 30k + -5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 6k + -1k2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + k)' equal to zero and attempt to solve:

Simplifying
-3 + k = 0

Solving
-3 + k = 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 + k = 0 + 3

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

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

Simplifying
k = 3
Subproblem 2
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
Solution
k = {3, 3}