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

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

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

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

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

Multiply (-8 + 3k) * (-3 + k)
(-8(-3 + k) + 3k * (-3 + k)) = 0
((-3 * -8 + k * -8) + 3k * (-3 + k)) = 0
((24 + -8k) + 3k * (-3 + k)) = 0
(24 + -8k + (-3 * 3k + k * 3k)) = 0
(24 + -8k + (-9k + 3k2)) = 0

Combine like terms: -8k + -9k = -17k
(24 + -17k + 3k2) = 0

Solving
24 + -17k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(8 + -3k)(3 + -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 '(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 = {2.666666667, 3}