3k^2-24=-14k

Solution for 3k^2-24=-14k equation:

Simplifying
3k2 + -24 = -14k

Reorder the terms:
-24 + 3k2 = -14k

Solving
-24 + 3k2 = -14k

Solving for variable 'k'.

Reorder the terms:
-24 + 14k + 3k2 = -14k + 14k

Combine like terms: -14k + 14k = 0
-24 + 14k + 3k2 = 0

Factor a trinomial.
(-6 + -1k)(4 + -3k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(4 + -3k)' equal to zero and attempt to solve:

Simplifying
4 + -3k = 0

Solving
4 + -3k = 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 + -3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3k = 0 + -4
-3k = 0 + -4

Combine like terms: 0 + -4 = -4
-3k = -4

Divide each side by '-3'.
k = 1.333333333

Simplifying
k = 1.333333333
Solution
k = {-6, 1.333333333}