k^2+9k=10

Solution for k^2+9k=10 equation:

Simplifying
k2 + 9k = 10

Reorder the terms:
9k + k2 = 10

Solving
9k + k2 = 10

Solving for variable 'k'.

Reorder the terms:
-10 + 9k + k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 9k + k2 = 0

Factor a trinomial.
(-10 + -1k)(1 + -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 '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {-10, 1}