k^2+10k-89=7

Solution for k^2+10k-89=7 equation:

Simplifying
k2 + 10k + -89 = 7

Reorder the terms:
-89 + 10k + k2 = 7

Solving
-89 + 10k + k2 = 7

Solving for variable 'k'.

Reorder the terms:
-89 + -7 + 10k + k2 = 7 + -7

Combine like terms: -89 + -7 = -96
-96 + 10k + k2 = 7 + -7

Combine like terms: 7 + -7 = 0
-96 + 10k + k2 = 0

Factor a trinomial.
(-16 + -1k)(6 + -1k) = 0

Subproblem 1
Set the factor '(-16 + -1k)' equal to zero and attempt to solve:

Simplifying
-16 + -1k = 0

Solving
-16 + -1k = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1k = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1k = 0 + 16
-1k = 0 + 16

Combine like terms: 0 + 16 = 16
-1k = 16

Divide each side by '-1'.
k = -16

Simplifying
k = -16
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 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 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-16, 6}