(13k+15)(k+13)=167

Solution for (13k+15)(k+13)=167 equation:

Simplifying
(13k + 15)(k + 13) = 167

Reorder the terms:
(15 + 13k)(k + 13) = 167

Reorder the terms:
(15 + 13k)(13 + k) = 167

Multiply (15 + 13k) * (13 + k)
(15(13 + k) + 13k * (13 + k)) = 167
((13 * 15 + k * 15) + 13k * (13 + k)) = 167
((195 + 15k) + 13k * (13 + k)) = 167
(195 + 15k + (13 * 13k + k * 13k)) = 167
(195 + 15k + (169k + 13k2)) = 167

Combine like terms: 15k + 169k = 184k
(195 + 184k + 13k2) = 167

Solving
195 + 184k + 13k2 = 167

Solving for variable 'k'.

Reorder the terms:
195 + -167 + 184k + 13k2 = 167 + -167

Combine like terms: 195 + -167 = 28
28 + 184k + 13k2 = 167 + -167

Combine like terms: 167 + -167 = 0
28 + 184k + 13k2 = 0

Factor a trinomial.
(14 + k)(2 + 13k) = 0

Subproblem 1
Set the factor '(14 + k)' equal to zero and attempt to solve:

Simplifying
14 + k = 0

Solving
14 + k = 0

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

Add '-14' to each side of the equation.
14 + -14 + k = 0 + -14

Combine like terms: 14 + -14 = 0
0 + k = 0 + -14
k = 0 + -14

Combine like terms: 0 + -14 = -14
k = -14

Simplifying
k = -14
Subproblem 2
Set the factor '(2 + 13k)' equal to zero and attempt to solve:

Simplifying
2 + 13k = 0

Solving
2 + 13k = 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 + 13k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 13k = 0 + -2
13k = 0 + -2

Combine like terms: 0 + -2 = -2
13k = -2

Divide each side by '13'.
k = -0.1538461538

Simplifying
k = -0.1538461538
Solution
k = {-14, -0.1538461538}