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

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


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

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

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

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

Combine like terms: -6k + 8k = 2k
(-16 + 2k + 3k2) = 0

Solving
-16 + 2k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-8 + -3k)(2 + -1k) = 0


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 '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 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 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-2.666666667, 2}

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