3k^2+6k=45

Solution for 3k^2+6k=45 equation:

Simplifying
3k2 + 6k = 45

Reorder the terms:
6k + 3k2 = 45

Solving
6k + 3k2 = 45

Solving for variable 'k'.

Reorder the terms:
-45 + 6k + 3k2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 6k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 2k + k2) = 0

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

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

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
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 = {-5, 3}