0=2k^2+k-3

Solution for 0=2k^2+k-3 equation:

Simplifying
0 = 2k2 + k + -3

Reorder the terms:
0 = -3 + k + 2k2

Solving
0 = -3 + k + 2k2

Solving for variable 'k'.

Combine like terms: 0 + 3 = 3
3 + -1k + -2k2 = -3 + k + 2k2 + 3 + -1k + -2k2

Reorder the terms:
3 + -1k + -2k2 = -3 + 3 + k + -1k + 2k2 + -2k2

Combine like terms: -3 + 3 = 0
3 + -1k + -2k2 = 0 + k + -1k + 2k2 + -2k2
3 + -1k + -2k2 = k + -1k + 2k2 + -2k2

Combine like terms: k + -1k = 0
3 + -1k + -2k2 = 0 + 2k2 + -2k2
3 + -1k + -2k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
3 + -1k + -2k2 = 0

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

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

Simplifying
1 + -1k = 0

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

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

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

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

Simplifying
k = 1
Subproblem 2
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
Solution
k = {1, -1.5}