ax^4-a^2x^3-6a^3x^2=

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Solution for ax^4-a^2x^3-6a^3x^2= equation: 


Simplifying
ax4 + -1a2x3 + -6a3x2 = 0

Solving
ax4 + -1a2x3 + -6a3x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ax2'.
ax2(x2 + -1ax + -6a2) = 0

Factor a trinomial.
ax2((x + -3a)(x + 2a)) = 0


Subproblem 1
Set the factor 'ax2' equal to zero and attempt to solve:

Simplifying
ax2 = 0

Solving
ax2 = 0

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

Simplifying
ax2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
x + -3a = 0

Reorder the terms:
-3a + x = 0

Solving
-3a + x = 0

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

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

Combine like terms: x + -1x = 0
-3a + 0 = 0 + -1x
-3a = 0 + -1x
Remove the zero:
-3a = -1x

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

Simplifying
a = 0.3333333333x

Subproblem 3
Set the factor '(x + 2a)' equal to zero and attempt to solve:

Simplifying
x + 2a = 0

Reorder the terms:
2a + x = 0

Solving
2a + x = 0

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

Add '-1x' to each side of the equation.
2a + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2a + 0 = 0 + -1x
2a = 0 + -1x
Remove the zero:
2a = -1x

Divide each side by '2'.
a = -0.5x

Simplifying
a = -0.5x
Solution
a = {0.3333333333x, -0.5x}

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