8(k+1)=4(k+1)(k+2)

Solution for 8(k+1)=4(k+1)(k+2) equation:

Simplifying
8(k + 1) = 4(k + 1)(k + 2)

Reorder the terms:
8(1 + k) = 4(k + 1)(k + 2)
(1 * 8 + k * 8) = 4(k + 1)(k + 2)
(8 + 8k) = 4(k + 1)(k + 2)

Reorder the terms:
8 + 8k = 4(1 + k)(k + 2)

Reorder the terms:
8 + 8k = 4(1 + k)(2 + k)

Multiply (1 + k) * (2 + k)
8 + 8k = 4(1(2 + k) + k(2 + k))
8 + 8k = 4((2 * 1 + k * 1) + k(2 + k))
8 + 8k = 4((2 + 1k) + k(2 + k))
8 + 8k = 4(2 + 1k + (2 * k + k * k))
8 + 8k = 4(2 + 1k + (2k + k2))

Combine like terms: 1k + 2k = 3k
8 + 8k = 4(2 + 3k + k2)
8 + 8k = (2 * 4 + 3k * 4 + k2 * 4)
8 + 8k = (8 + 12k + 4k2)

Add '-8' to each side of the equation.
8 + -8 + 8k = 8 + 12k + -8 + 4k2

Combine like terms: 8 + -8 = 0
0 + 8k = 8 + 12k + -8 + 4k2
8k = 8 + 12k + -8 + 4k2

Reorder the terms:
8k = 8 + -8 + 12k + 4k2

Combine like terms: 8 + -8 = 0
8k = 0 + 12k + 4k2
8k = 12k + 4k2

Solving
8k = 12k + 4k2

Solving for variable 'k'.

Combine like terms: 8k + -12k = -4k
-4k + -4k2 = 12k + 4k2 + -12k + -4k2

Reorder the terms:
-4k + -4k2 = 12k + -12k + 4k2 + -4k2

Combine like terms: 12k + -12k = 0
-4k + -4k2 = 0 + 4k2 + -4k2
-4k + -4k2 = 4k2 + -4k2

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

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

Ignore the factor -4.
Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
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 = {0, -1}