20k(k+2)=3k-15

Solution for 20k(k+2)=3k-15 equation:

Simplifying
20k(k + 2) = 3k + -15

Reorder the terms:
20k(2 + k) = 3k + -15
(2 * 20k + k * 20k) = 3k + -15
(40k + 20k2) = 3k + -15

Reorder the terms:
40k + 20k2 = -15 + 3k

Solving
40k + 20k2 = -15 + 3k

Solving for variable 'k'.

Reorder the terms:
15 + 40k + -3k + 20k2 = -15 + 3k + 15 + -3k

Combine like terms: 40k + -3k = 37k
15 + 37k + 20k2 = -15 + 3k + 15 + -3k

Reorder the terms:
15 + 37k + 20k2 = -15 + 15 + 3k + -3k

Combine like terms: -15 + 15 = 0
15 + 37k + 20k2 = 0 + 3k + -3k
15 + 37k + 20k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
15 + 37k + 20k2 = 0

Factor a trinomial.
(5 + 4k)(3 + 5k) = 0

Subproblem 1
Set the factor '(5 + 4k)' equal to zero and attempt to solve:

Simplifying
5 + 4k = 0

Solving
5 + 4k = 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 + 4k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4k = 0 + -5
4k = 0 + -5

Combine like terms: 0 + -5 = -5
4k = -5

Divide each side by '4'.
k = -1.25

Simplifying
k = -1.25
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 = {-1.25, -0.6}