(5k+7)(k+5)=23

Solution for (5k+7)(k+5)=23 equation:

Simplifying
(5k + 7)(k + 5) = 23

Reorder the terms:
(7 + 5k)(k + 5) = 23

Reorder the terms:
(7 + 5k)(5 + k) = 23

Multiply (7 + 5k) * (5 + k)
(7(5 + k) + 5k * (5 + k)) = 23
((5 * 7 + k * 7) + 5k * (5 + k)) = 23
((35 + 7k) + 5k * (5 + k)) = 23
(35 + 7k + (5 * 5k + k * 5k)) = 23
(35 + 7k + (25k + 5k2)) = 23

Combine like terms: 7k + 25k = 32k
(35 + 32k + 5k2) = 23

Solving
35 + 32k + 5k2 = 23

Solving for variable 'k'.

Reorder the terms:
35 + -23 + 32k + 5k2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32k + 5k2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32k + 5k2 = 0

Factor a trinomial.
(6 + k)(2 + 5k) = 0

Subproblem 1
Set the factor '(6 + k)' equal to zero and attempt to solve:

Simplifying
6 + k = 0

Solving
6 + k = 0

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

Add '-6' to each side of the equation.
6 + -6 + k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + k = 0 + -6
k = 0 + -6

Combine like terms: 0 + -6 = -6
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(2 + 5k)' equal to zero and attempt to solve:

Simplifying
2 + 5k = 0

Solving
2 + 5k = 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 + 5k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5k = 0 + -2
5k = 0 + -2

Combine like terms: 0 + -2 = -2
5k = -2

Divide each side by '5'.
k = -0.4

Simplifying
k = -0.4
Solution
k = {-6, -0.4}