45k+27=18k^2

Solution for 45k+27=18k^2 equation:

Simplifying
45k + 27 = 18k2

Reorder the terms:
27 + 45k = 18k2

Solving
27 + 45k = 18k2

Solving for variable 'k'.

Combine like terms: 18k2 + -18k2 = 0
27 + 45k + -18k2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(3 + 5k + -2k2) = 0

Factor a trinomial.
9((3 + -1k)(1 + 2k)) = 0

Ignore the factor 9.
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 '(1 + 2k)' equal to zero and attempt to solve:

Simplifying
1 + 2k = 0

Solving
1 + 2k = 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 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Solution
k = {3, -0.5}