72+27a+a^2=0

Solution for 72+27a+a^2=0 equation:

Simplifying
72 + 27a + a2 = 0

Solving
72 + 27a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(24 + a)(3 + a) = 0

Subproblem 1
Set the factor '(24 + a)' equal to zero and attempt to solve:

Simplifying
24 + a = 0

Solving
24 + a = 0

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

Add '-24' to each side of the equation.
24 + -24 + a = 0 + -24

Combine like terms: 24 + -24 = 0
0 + a = 0 + -24
a = 0 + -24

Combine like terms: 0 + -24 = -24
a = -24

Simplifying
a = -24
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {-24, -3}