(3k-2)(3k-2)=49

Solution for (3k-2)(3k-2)=49 equation:

Simplifying
(3k + -2)(3k + -2) = 49

Reorder the terms:
(-2 + 3k)(3k + -2) = 49

Reorder the terms:
(-2 + 3k)(-2 + 3k) = 49

Multiply (-2 + 3k) * (-2 + 3k)
(-2(-2 + 3k) + 3k * (-2 + 3k)) = 49
((-2 * -2 + 3k * -2) + 3k * (-2 + 3k)) = 49
((4 + -6k) + 3k * (-2 + 3k)) = 49
(4 + -6k + (-2 * 3k + 3k * 3k)) = 49
(4 + -6k + (-6k + 9k2)) = 49

Combine like terms: -6k + -6k = -12k
(4 + -12k + 9k2) = 49

Solving
4 + -12k + 9k2 = 49

Solving for variable 'k'.

Reorder the terms:
4 + -49 + -12k + 9k2 = 49 + -49

Combine like terms: 4 + -49 = -45
-45 + -12k + 9k2 = 49 + -49

Combine like terms: 49 + -49 = 0
-45 + -12k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -4k + 3k2) = 0

Factor a trinomial.
3((-5 + -3k)(3 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -3k)' equal to zero and attempt to solve:

Simplifying
-5 + -3k = 0

Solving
-5 + -3k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3k = 0 + 5
-3k = 0 + 5

Combine like terms: 0 + 5 = 5
-3k = 5

Divide each side by '-3'.
k = -1.666666667

Simplifying
k = -1.666666667
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 = {-1.666666667, 3}