k^2+2k-75=5

Solution for k^2+2k-75=5 equation:

Simplifying
k2 + 2k + -75 = 5

Reorder the terms:
-75 + 2k + k2 = 5

Solving
-75 + 2k + k2 = 5

Solving for variable 'k'.

Reorder the terms:
-75 + -5 + 2k + k2 = 5 + -5

Combine like terms: -75 + -5 = -80
-80 + 2k + k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-80 + 2k + k2 = 0

Factor a trinomial.
(-10 + -1k)(8 + -1k) = 0

Subproblem 1
Set the factor '(-10 + -1k)' equal to zero and attempt to solve:

Simplifying
-10 + -1k = 0

Solving
-10 + -1k = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1k = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1k = 0 + 10
-1k = 0 + 10

Combine like terms: 0 + 10 = 10
-1k = 10

Divide each side by '-1'.
k = -10

Simplifying
k = -10
Subproblem 2
Set the factor '(8 + -1k)' equal to zero and attempt to solve:

Simplifying
8 + -1k = 0

Solving
8 + -1k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1k = 0 + -8
-1k = 0 + -8

Combine like terms: 0 + -8 = -8
-1k = -8

Divide each side by '-1'.
k = 8

Simplifying
k = 8
Solution
k = {-10, 8}