(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((-1 + -3k)(3 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
k = {-0.3333333333, 3}