a^2-18a=19

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

Simplifying
a2 + -18a = 19

Reorder the terms:
-18a + a2 = 19

Solving
-18a + a2 = 19

Solving for variable 'a'.

Reorder the terms:
-19 + -18a + a2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + -18a + a2 = 0

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

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

Simplifying
19 + -1a = 0

Solving
19 + -1a = 0

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

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

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

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

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

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