(3k+2)(3k+2)=100

Solution for (3k+2)(3k+2)=100 equation:

Simplifying
(3k + 2)(3k + 2) = 100

Reorder the terms:
(2 + 3k)(3k + 2) = 100

Reorder the terms:
(2 + 3k)(2 + 3k) = 100

Multiply (2 + 3k) * (2 + 3k)
(2(2 + 3k) + 3k * (2 + 3k)) = 100
((2 * 2 + 3k * 2) + 3k * (2 + 3k)) = 100
((4 + 6k) + 3k * (2 + 3k)) = 100
(4 + 6k + (2 * 3k + 3k * 3k)) = 100
(4 + 6k + (6k + 9k2)) = 100

Combine like terms: 6k + 6k = 12k
(4 + 12k + 9k2) = 100

Solving
4 + 12k + 9k2 = 100

Solving for variable 'k'.

Reorder the terms:
4 + -100 + 12k + 9k2 = 100 + -100

Combine like terms: 4 + -100 = -96
-96 + 12k + 9k2 = 100 + -100

Combine like terms: 100 + -100 = 0
-96 + 12k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + 4k + 3k2) = 0

Factor a trinomial.
3((-4 + -1k)(8 + -3k)) = 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 '(8 + -3k)' equal to zero and attempt to solve:

Simplifying
8 + -3k = 0

Solving
8 + -3k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3k = 0 + -8
-3k = 0 + -8

Combine like terms: 0 + -8 = -8
-3k = -8

Divide each side by '-3'.
k = 2.666666667

Simplifying
k = 2.666666667
Solution
k = {-4, 2.666666667}