12a^4b^3-36a^3b^4+27a^2b^5=

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Solution for 12a^4b^3-36a^3b^4+27a^2b^5= equation: 


Simplifying
12a4b3 + -36a3b4 + 27a2b5 = 0

Reorder the terms:
27a2b5 + -36a3b4 + 12a4b3 = 0

Solving
27a2b5 + -36a3b4 + 12a4b3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a2b3'.
3a2b3(9b2 + -12ab + 4a2) = 0

Factor a trinomial.
3a2b3((3b + -2a)(3b + -2a)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'a2b3' equal to zero and attempt to solve:

Simplifying
a2b3 = 0

Solving
a2b3 = 0

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

Simplifying
a2b3 = 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 '(3b + -2a)' equal to zero and attempt to solve:

Simplifying
3b + -2a = 0

Reorder the terms:
-2a + 3b = 0

Solving
-2a + 3b = 0

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

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

Combine like terms: 3b + -3b = 0
-2a + 0 = 0 + -3b
-2a = 0 + -3b
Remove the zero:
-2a = -3b

Divide each side by '-2'.
a = 1.5b

Simplifying
a = 1.5b

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

Simplifying
3b + -2a = 0

Reorder the terms:
-2a + 3b = 0

Solving
-2a + 3b = 0

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

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

Combine like terms: 3b + -3b = 0
-2a + 0 = 0 + -3b
-2a = 0 + -3b
Remove the zero:
-2a = -3b

Divide each side by '-2'.
a = 1.5b

Simplifying
a = 1.5b
Solution
a = {1.5b, 1.5b}

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