(3k-2)(6k+8)=0

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Solution for (3k-2)(6k+8)=0 equation: 


Simplifying
(3k + -2)(6k + 8) = 0

Reorder the terms:
(-2 + 3k)(6k + 8) = 0

Reorder the terms:
(-2 + 3k)(8 + 6k) = 0

Multiply (-2 + 3k) * (8 + 6k)
(-2(8 + 6k) + 3k * (8 + 6k)) = 0
((8 * -2 + 6k * -2) + 3k * (8 + 6k)) = 0
((-16 + -12k) + 3k * (8 + 6k)) = 0
(-16 + -12k + (8 * 3k + 6k * 3k)) = 0
(-16 + -12k + (24k + 18k2)) = 0

Combine like terms: -12k + 24k = 12k
(-16 + 12k + 18k2) = 0

Solving
-16 + 12k + 18k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 6k + 9k2) = 0

Factor a trinomial.
2((-4 + -3k)(2 + -3k)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3k)' equal to zero and attempt to solve:

Simplifying
-4 + -3k = 0

Solving
-4 + -3k = 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 + -3k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3k = 0 + 4
-3k = 0 + 4

Combine like terms: 0 + 4 = 4
-3k = 4

Divide each side by '-3'.
k = -1.333333333

Simplifying
k = -1.333333333

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

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-1.333333333, 0.6666666667}

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