(3k+4)(3k+4)=25

Solution for (3k+4)(3k+4)=25 equation:

Simplifying
(3k + 4)(3k + 4) = 25

Reorder the terms:
(4 + 3k)(3k + 4) = 25

Reorder the terms:
(4 + 3k)(4 + 3k) = 25

Multiply (4 + 3k) * (4 + 3k)
(4(4 + 3k) + 3k * (4 + 3k)) = 25
((4 * 4 + 3k * 4) + 3k * (4 + 3k)) = 25
((16 + 12k) + 3k * (4 + 3k)) = 25
(16 + 12k + (4 * 3k + 3k * 3k)) = 25
(16 + 12k + (12k + 9k2)) = 25

Combine like terms: 12k + 12k = 24k
(16 + 24k + 9k2) = 25

Solving
16 + 24k + 9k2 = 25

Solving for variable 'k'.

Reorder the terms:
16 + -25 + 24k + 9k2 = 25 + -25

Combine like terms: 16 + -25 = -9
-9 + 24k + 9k2 = 25 + -25

Combine like terms: 25 + -25 = 0
-9 + 24k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 8k + 3k2) = 0

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

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

Simplifying
-3 + -1k = 0

Solving
-3 + -1k = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1k = 0 + 3
-1k = 0 + 3

Combine like terms: 0 + 3 = 3
-1k = 3

Divide each side by '-1'.
k = -3

Simplifying
k = -3
Subproblem 2
Set the factor '(1 + -3k)' equal to zero and attempt to solve:

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3k = 0 + -1
-3k = 0 + -1

Combine like terms: 0 + -1 = -1
-3k = -1

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Solution
k = {-3, 0.3333333333}