a^2+15a=54

Solution for a^2+15a=54 equation:

Simplifying
a2 + 15a = 54

Reorder the terms:
15a + a2 = 54

Solving
15a + a2 = 54

Solving for variable 'a'.

Reorder the terms:
-54 + 15a + a2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 15a + a2 = 0

Factor a trinomial.
(-18 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-18 + -1a)' equal to zero and attempt to solve:

Simplifying
-18 + -1a = 0

Solving
-18 + -1a = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1a = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1a = 0 + 18
-1a = 0 + 18

Combine like terms: 0 + 18 = 18
-1a = 18

Divide each side by '-1'.
a = -18

Simplifying
a = -18
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-18, 3}