3k^2+2k=16

Solution for 3k^2+2k=16 equation:

Simplifying
3k2 + 2k = 16

Reorder the terms:
2k + 3k2 = 16

Solving
2k + 3k2 = 16

Solving for variable 'k'.

Reorder the terms:
-16 + 2k + 3k2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 2k + 3k2 = 0

Factor a trinomial.
(-8 + -3k)(2 + -1k) = 0

Subproblem 1
Set the factor '(-8 + -3k)' equal to zero and attempt to solve:

Simplifying
-8 + -3k = 0

Solving
-8 + -3k = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3k = 0 + 8
-3k = 0 + 8

Combine like terms: 0 + 8 = 8
-3k = 8

Divide each side by '-3'.
k = -2.666666667

Simplifying
k = -2.666666667
Subproblem 2
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
Solution
k = {-2.666666667, 2}