k^2-18k=19

Solution for k^2-18k=19 equation:

Simplifying
k2 + -18k = 19

Reorder the terms:
-18k + k2 = 19

Solving
-18k + k2 = 19

Solving for variable 'k'.

Reorder the terms:
-19 + -18k + k2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + -18k + k2 = 0

Factor a trinomial.
(-1 + -1k)(19 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(19 + -1k)' equal to zero and attempt to solve:

Simplifying
19 + -1k = 0

Solving
19 + -1k = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1k = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1k = 0 + -19
-1k = 0 + -19

Combine like terms: 0 + -19 = -19
-1k = -19

Divide each side by '-1'.
k = 19

Simplifying
k = 19
Solution
k = {-1, 19}