3a^4+3a^3+36a^2=

Solution for 3a^4+3a^3+36a^2= equation:

Simplifying
3a4 + 3a3 + 36a2 = 0

Reorder the terms:
36a2 + 3a3 + 3a4 = 0

Solving
36a2 + 3a3 + 3a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a2'.
3a2(12 + a + a2) = 0

Ignore the factor 3.
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 '(12 + a + a2)' equal to zero and attempt to solve:

Simplifying
12 + a + a2 = 0

Solving
12 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + a + -12 + a2 = 0 + -12

Reorder the terms:
12 + -12 + a + a2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + a + a2 = 0 + -12
a + a2 = 0 + -12

Combine like terms: 0 + -12 = -12
a + a2 = -12

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
a + 0.25 + a2 = -12 + 0.25

Reorder the terms:
0.25 + a + a2 = -12 + 0.25

Combine like terms: -12 + 0.25 = -11.75
0.25 + a + a2 = -11.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -11.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}