3k^2+5k=2

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

Simplifying
3k2 + 5k = 2

Reorder the terms:
5k + 3k2 = 2

Solving
5k + 3k2 = 2

Solving for variable 'k'.

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

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

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

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

Simplifying
-2 + -1k = 0

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

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

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

Divide each side by '-1'.
k = -2

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

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

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

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

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Solution
k = {-2, 0.3333333333}