2k^2-5=9k

Solution for 2k^2-5=9k equation:

Simplifying
2k2 + -5 = 9k

Reorder the terms:
-5 + 2k2 = 9k

Solving
-5 + 2k2 = 9k

Solving for variable 'k'.

Reorder the terms:
-5 + -9k + 2k2 = 9k + -9k

Combine like terms: 9k + -9k = 0
-5 + -9k + 2k2 = 0

Factor a trinomial.
(-1 + -2k)(5 + -1k) = 0

Subproblem 1
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
Subproblem 2
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
Solution
k = {-0.5, 5}