-3k(k-5)+[-6(k+1)+18]=

Solution for -3k(k-5)+[-6(k+1)+18]= equation:

Simplifying
-3k(k + -5) + [-6(k + 1) + 18] = 0

Reorder the terms:
-3k(-5 + k) + [-6(k + 1) + 18] = 0
(-5 * -3k + k * -3k) + [-6(k + 1) + 18] = 0
(15k + -3k2) + [-6(k + 1) + 18] = 0

Reorder the terms:
15k + -3k2 + [-6(1 + k) + 18] = 0
15k + -3k2 + [(1 * -6 + k * -6) + 18] = 0
15k + -3k2 + [(-6 + -6k) + 18] = 0

Reorder the terms:
15k + -3k2 + [-6 + 18 + -6k] = 0

Combine like terms: -6 + 18 = 12
15k + -3k2 + [12 + -6k] = 0

Remove brackets around [12 + -6k]
15k + -3k2 + 12 + -6k = 0

Reorder the terms:
12 + 15k + -6k + -3k2 = 0

Combine like terms: 15k + -6k = 9k
12 + 9k + -3k2 = 0

Solving
12 + 9k + -3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 3k + -1k2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

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

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

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

Simplifying
k = -1
Solution
k = {4, -1}