12ay^2+31ay+20a=0

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Solution for 12ay^2+31ay+20a=0 equation: 


Simplifying
12ay2 + 31ay + 20a = 0

Reorder the terms:
20a + 31ay + 12ay2 = 0

Solving
20a + 31ay + 12ay2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(20 + 31y + 12y2) = 0

Factor a trinomial.
a((4 + 3y)(5 + 4y)) = 0


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Add '-3y' to each side of the equation.
3y + -3y = -4 + -3y

Combine like terms: 3y + -3y = 0
0 = -4 + -3y

Simplifying
0 = -4 + -3y

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 '(5 + 4y)' equal to zero and attempt to solve:

Simplifying
5 + 4y = 0

Solving
5 + 4y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4y = 0 + -5
4y = 0 + -5

Combine like terms: 0 + -5 = -5
4y = -5

Add '-4y' to each side of the equation.
4y + -4y = -5 + -4y

Combine like terms: 4y + -4y = 0
0 = -5 + -4y

Simplifying
0 = -5 + -4y

The solution to this equation could not be determined.

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

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