4*a^2-9*a^6=

Solution for 4*a^2-9*a^6= equation:

Simplifying
4a2 + -9a6 = 0

Solving
4a2 + -9a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(4 + -9a4) = 0

Factor a difference between two squares.
a2((2 + 3a2)(2 + -3a2)) = 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 '(2 + 3a2)' equal to zero and attempt to solve:

Simplifying
2 + 3a2 = 0

Solving
2 + 3a2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a2 = 0 + -2
3a2 = 0 + -2

Combine like terms: 0 + -2 = -2
3a2 = -2

Divide each side by '3'.
a2 = -0.6666666667

Simplifying
a2 = -0.6666666667

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + -3a2)' equal to zero and attempt to solve:

Simplifying
2 + -3a2 = 0

Solving
2 + -3a2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a2 = 0 + -2
-3a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3a2 = -2

Divide each side by '-3'.
a2 = 0.6666666667

Simplifying
a2 = 0.6666666667

Take the square root of each side:
a = {-0.816496581, 0.816496581}
Solution
a = {0, -0.816496581, 0.816496581}