=54+15a+a^2

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

Simplifying
0 = 54 + 15a + a2

Solving
0 = 54 + 15a + a2

Solving for variable 'a'.

Combine like terms: 0 + -54 = -54
-54 + -15a + -1a2 = 54 + 15a + a2 + -54 + -15a + -1a2

Reorder the terms:
-54 + -15a + -1a2 = 54 + -54 + 15a + -15a + a2 + -1a2

Combine like terms: 54 + -54 = 0
-54 + -15a + -1a2 = 0 + 15a + -15a + a2 + -1a2
-54 + -15a + -1a2 = 15a + -15a + a2 + -1a2

Combine like terms: 15a + -15a = 0
-54 + -15a + -1a2 = 0 + a2 + -1a2
-54 + -15a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-54 + -15a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(54 + 15a + a2) = 0

Factor a trinomial.
-1((9 + a)(6 + a)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + a)' equal to zero and attempt to solve:

Simplifying
9 + a = 0

Solving
9 + a = 0

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

Add '-9' to each side of the equation.
9 + -9 + a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + a = 0 + -9
a = 0 + -9

Combine like terms: 0 + -9 = -9
a = -9

Simplifying
a = -9
Subproblem 2
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {-9, -6}