3k^2=-32+20k

Solution for 3k^2=-32+20k equation:

Simplifying
3k2 = -32 + 20k

Solving
3k2 = -32 + 20k

Solving for variable 'k'.

Reorder the terms:
32 + -20k + 3k2 = -32 + 20k + 32 + -20k

Reorder the terms:
32 + -20k + 3k2 = -32 + 32 + 20k + -20k

Combine like terms: -32 + 32 = 0
32 + -20k + 3k2 = 0 + 20k + -20k
32 + -20k + 3k2 = 20k + -20k

Combine like terms: 20k + -20k = 0
32 + -20k + 3k2 = 0

Factor a trinomial.
(8 + -3k)(4 + -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 '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {2.666666667, 4}