3k^2=5k-2

Solution for 3k^2=5k-2 equation:

Simplifying
3k2 = 5k + -2

Reorder the terms:
3k2 = -2 + 5k

Solving
3k2 = -2 + 5k

Solving for variable 'k'.

Reorder the terms:
2 + -5k + 3k2 = -2 + 5k + 2 + -5k

Reorder the terms:
2 + -5k + 3k2 = -2 + 2 + 5k + -5k

Combine like terms: -2 + 2 = 0
2 + -5k + 3k2 = 0 + 5k + -5k
2 + -5k + 3k2 = 5k + -5k

Combine like terms: 5k + -5k = 0
2 + -5k + 3k2 = 0

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

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

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

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

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

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Subproblem 2
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
Solution
k = {0.6666666667, 1}