2a^2+21a+54=0

Solution for 2a^2+21a+54=0 equation:

Simplifying
2a2 + 21a + 54 = 0

Reorder the terms:
54 + 21a + 2a2 = 0

Solving
54 + 21a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(9 + 2a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + 2a)' equal to zero and attempt to solve:

Simplifying
9 + 2a = 0

Solving
9 + 2a = 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 + 2a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2a = 0 + -9
2a = 0 + -9

Combine like terms: 0 + -9 = -9
2a = -9

Divide each side by '2'.
a = -4.5

Simplifying
a = -4.5
Solution
a = {-6, -4.5}