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

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

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

Reorder the terms:
-3(1 + k)[(k + 1) + -5] = 0

Reorder the terms:
-3(1 + k)[(1 + k) + -5] = 0

Remove parenthesis around (1 + k)
-3(1 + k)[1 + k + -5] = 0

Reorder the terms:
-3(1 + k)[1 + -5 + k] = 0

Combine like terms: 1 + -5 = -4
-3(1 + k)[-4 + k] = 0

Multiply (1 + k) * [-4 + k]
-3(1[-4 + k] + k[-4 + k]) = 0
-3([-4 * 1 + k * 1] + k[-4 + k]) = 0
-3([-4 + 1k] + k[-4 + k]) = 0
-3(-4 + 1k + [-4 * k + k * k]) = 0
-3(-4 + 1k + [-4k + k2]) = 0

Combine like terms: 1k + -4k = -3k
-3(-4 + -3k + k2) = 0
(-4 * -3 + -3k * -3 + k2 * -3) = 0
(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}