(18a^4)+(27a^3)+(7a^2)=0

Solution for (18a^4)+(27a^3)+(7a^2)=0 equation:

Simplifying
(18a4) + (27a3) + (7a2) = 0

Reorder the terms:
(7a2) + (27a3) + (18a4) = 0

Solving
(7a2) + (27a3) + (18a4) = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(7 + (27a) + (18a2)) = 0

Factor a trinomial.
a2((7 + 6a)(1 + 3a)) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(7 + 6a)' equal to zero and attempt to solve:

Simplifying
7 + 6a = 0

Solving
7 + 6a = 0

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

Add '-7' to each side of the equation.
7 + -7 + 6a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6a = 0 + -7
6a = 0 + -7

Combine like terms: 0 + -7 = -7
6a = -7

Divide each side by '6'.
a = -1.166666667

Simplifying
a = -1.166666667
Subproblem 3
Set the factor '(1 + 3a)' equal to zero and attempt to solve:

Simplifying
1 + 3a = 0

Solving
1 + 3a = 0

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

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

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

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

Divide each side by '3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Solution
a = {0, -1.166666667, -0.3333333333}