(k-5)(3k+2)=0

Solution for (k-5)(3k+2)=0 equation:

Simplifying
(k + -5)(3k + 2) = 0

Reorder the terms:
(-5 + k)(3k + 2) = 0

Reorder the terms:
(-5 + k)(2 + 3k) = 0

Multiply (-5 + k) * (2 + 3k)
(-5(2 + 3k) + k(2 + 3k)) = 0
((2 * -5 + 3k * -5) + k(2 + 3k)) = 0
((-10 + -15k) + k(2 + 3k)) = 0
(-10 + -15k + (2 * k + 3k * k)) = 0
(-10 + -15k + (2k + 3k2)) = 0

Combine like terms: -15k + 2k = -13k
(-10 + -13k + 3k2) = 0

Solving
-10 + -13k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-2 + -3k)(5 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {-0.6666666667, 5}