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

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

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

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

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

Multiply (-3 + 5k) * (5 + k)
(-3(5 + k) + 5k * (5 + k)) = 0
((5 * -3 + k * -3) + 5k * (5 + k)) = 0
((-15 + -3k) + 5k * (5 + k)) = 0
(-15 + -3k + (5 * 5k + k * 5k)) = 0
(-15 + -3k + (25k + 5k2)) = 0

Combine like terms: -3k + 25k = 22k
(-15 + 22k + 5k2) = 0

Solving
-15 + 22k + 5k2 = 0

Solving for variable 'k'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -5k)' equal to zero and attempt to solve:

Simplifying
3 + -5k = 0

Solving
3 + -5k = 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 + -5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k = 0 + -3
-5k = 0 + -3

Combine like terms: 0 + -3 = -3
-5k = -3

Divide each side by '-5'.
k = 0.6

Simplifying
k = 0.6
Solution
k = {-5, 0.6}