a^2+8a=513

Solution for a^2+8a=513 equation:

Simplifying
a2 + 8a = 513

Reorder the terms:
8a + a2 = 513

Solving
8a + a2 = 513

Solving for variable 'a'.

Reorder the terms:
-513 + 8a + a2 = 513 + -513

Combine like terms: 513 + -513 = 0
-513 + 8a + a2 = 0

Factor a trinomial.
(-27 + -1a)(19 + -1a) = 0

Subproblem 1
Set the factor '(-27 + -1a)' equal to zero and attempt to solve:

Simplifying
-27 + -1a = 0

Solving
-27 + -1a = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1a = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1a = 0 + 27
-1a = 0 + 27

Combine like terms: 0 + 27 = 27
-1a = 27

Divide each side by '-1'.
a = -27

Simplifying
a = -27
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 = {-27, 19}