(3k-2)(3k-2)=100

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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((-8 + -3k)(4 + -1k)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
k = {-2.666666667, 4}

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