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

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

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

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

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

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

Combine like terms: 16k + -3k = 13k
(-24 + 13k + 2k2) = 0

Solving
-24 + 13k + 2k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve:

Simplifying
-8 + -1k = 0

Solving
-8 + -1k = 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 + -1k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1k = 0 + 8
-1k = 0 + 8

Combine like terms: 0 + 8 = 8
-1k = 8

Divide each side by '-1'.
k = -8

Simplifying
k = -8
Subproblem 2
Set the factor '(3 + -2k)' equal to zero and attempt to solve:

Simplifying
3 + -2k = 0

Solving
3 + -2k = 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 + -2k = 0 + -3

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

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

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Solution
k = {-8, 1.5}