6-k(k-3)=4k

Solution for 6-k(k-3)=4k equation:

Simplifying
6 + -1k(k + -3) = 4k

Reorder the terms:
6 + -1k(-3 + k) = 4k
6 + (-3 * -1k + k * -1k) = 4k
6 + (3k + -1k2) = 4k

Solving
6 + 3k + -1k2 = 4k

Solving for variable 'k'.

Reorder the terms:
6 + 3k + -4k + -1k2 = 4k + -4k

Combine like terms: 3k + -4k = -1k
6 + -1k + -1k2 = 4k + -4k

Combine like terms: 4k + -4k = 0
6 + -1k + -1k2 = 0

Factor a trinomial.
(2 + -1k)(3 + k) = 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 '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

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

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

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

Simplifying
k = -3
Solution
k = {2, -3}