3(k+2)(k+2)=5k+8

Solution for 3(k+2)(k+2)=5k+8 equation:

Simplifying
3(k + 2)(k + 2) = 5k + 8

Reorder the terms:
3(2 + k)(k + 2) = 5k + 8

Reorder the terms:
3(2 + k)(2 + k) = 5k + 8

Multiply (2 + k) * (2 + k)
3(2(2 + k) + k(2 + k)) = 5k + 8
3((2 * 2 + k * 2) + k(2 + k)) = 5k + 8
3((4 + 2k) + k(2 + k)) = 5k + 8
3(4 + 2k + (2 * k + k * k)) = 5k + 8
3(4 + 2k + (2k + k2)) = 5k + 8

Combine like terms: 2k + 2k = 4k
3(4 + 4k + k2) = 5k + 8
(4 * 3 + 4k * 3 + k2 * 3) = 5k + 8
(12 + 12k + 3k2) = 5k + 8

Reorder the terms:
12 + 12k + 3k2 = 8 + 5k

Solving
12 + 12k + 3k2 = 8 + 5k

Solving for variable 'k'.

Reorder the terms:
12 + -8 + 12k + -5k + 3k2 = 8 + 5k + -8 + -5k

Combine like terms: 12 + -8 = 4
4 + 12k + -5k + 3k2 = 8 + 5k + -8 + -5k

Combine like terms: 12k + -5k = 7k
4 + 7k + 3k2 = 8 + 5k + -8 + -5k

Reorder the terms:
4 + 7k + 3k2 = 8 + -8 + 5k + -5k

Combine like terms: 8 + -8 = 0
4 + 7k + 3k2 = 0 + 5k + -5k
4 + 7k + 3k2 = 5k + -5k

Combine like terms: 5k + -5k = 0
4 + 7k + 3k2 = 0

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

Subproblem 1
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
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 = {-1.333333333, -1}