36a^3b^2-10a^2b^2-12ab^2=

Solution for 36a^3b^2-10a^2b^2-12ab^2= equation:

Simplifying
36a3b2 + -10a2b2 + -12ab2 = 0

Reorder the terms:
-12ab2 + -10a2b2 + 36a3b2 = 0

Solving
-12ab2 + -10a2b2 + 36a3b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2ab2'.
2ab2(-6 + -5a + 18a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'ab2' equal to zero and attempt to solve:

Simplifying
ab2 = 0

Solving
ab2 = 0

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

Simplifying
ab2 = 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 '(-6 + -5a + 18a2)' equal to zero and attempt to solve:

Simplifying
-6 + -5a + 18a2 = 0

Solving
-6 + -5a + 18a2 = 0

Begin completing the square.  Divide all terms by
18 the coefficient of the squared term: 

Divide each side by '18'.
-0.3333333333 + -0.2777777778a + a2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.2777777778a + 0.3333333333 + a2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.2777777778a + a2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.2777777778a + a2 = 0 + 0.3333333333
-0.2777777778a + a2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.2777777778a + a2 = 0.3333333333

The a term is -0.2777777778a.  Take half its coefficient (-0.1388888889).
Square it (0.01929012346) and add it to both sides.

Add '0.01929012346' to each side of the equation.
-0.2777777778a + 0.01929012346 + a2 = 0.3333333333 + 0.01929012346

Reorder the terms:
0.01929012346 + -0.2777777778a + a2 = 0.3333333333 + 0.01929012346

Combine like terms: 0.3333333333 + 0.01929012346 = 0.35262345676
0.01929012346 + -0.2777777778a + a2 = 0.35262345676

Factor a perfect square on the left side:
(a + -0.1388888889)(a + -0.1388888889) = 0.35262345676

Calculate the square root of the right side: 0.593821065

Break this problem into two subproblems by setting 
(a + -0.1388888889) equal to 0.593821065 and -0.593821065.

Subproblem 1
a + -0.1388888889 = 0.593821065

Simplifying
a + -0.1388888889 = 0.593821065

Reorder the terms:
-0.1388888889 + a = 0.593821065

Solving
-0.1388888889 + a = 0.593821065

Solving for variable 'a'.

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

Add '0.1388888889' to each side of the equation.
-0.1388888889 + 0.1388888889 + a = 0.593821065 + 0.1388888889

Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000
0.0000000000 + a = 0.593821065 + 0.1388888889
a = 0.593821065 + 0.1388888889

Combine like terms: 0.593821065 + 0.1388888889 = 0.7327099539
a = 0.7327099539

Simplifying
a = 0.7327099539

Subproblem 2
a + -0.1388888889 = -0.593821065

Simplifying
a + -0.1388888889 = -0.593821065

Reorder the terms:
-0.1388888889 + a = -0.593821065

Solving
-0.1388888889 + a = -0.593821065

Solving for variable 'a'.

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

Add '0.1388888889' to each side of the equation.
-0.1388888889 + 0.1388888889 + a = -0.593821065 + 0.1388888889

Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000
0.0000000000 + a = -0.593821065 + 0.1388888889
a = -0.593821065 + 0.1388888889

Combine like terms: -0.593821065 + 0.1388888889 = -0.4549321761
a = -0.4549321761

Simplifying
a = -0.4549321761

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.7327099539, -0.4549321761}
Solution
a = {0.7327099539, -0.4549321761}