2k^2-3k=9

Solution for 2k^2-3k=9 equation:

Simplifying
2k2 + -3k = 9

Reorder the terms:
-3k + 2k2 = 9

Solving
-3k + 2k2 = 9

Solving for variable 'k'.

Reorder the terms:
-9 + -3k + 2k2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -3k + 2k2 = 0

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

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

Simplifying
-3 + -2k = 0

Solving
-3 + -2k = 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 + -2k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2k = 0 + 3
-2k = 0 + 3

Combine like terms: 0 + 3 = 3
-2k = 3

Divide each side by '-2'.
k = -1.5

Simplifying
k = -1.5
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 = {-1.5, 3}