12am^2+6amn-30am-15an=0

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Solution for 12am^2+6amn-30am-15an=0 equation: 


Simplifying
12am2 + 6amn + -30am + -15an = 0

Reorder the terms:
-30am + 6amn + 12am2 + -15an = 0

Solving
-30am + 6amn + 12am2 + -15an = 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), '3a'.
3a(-10m + 2mn + 4m2 + -5n) = 0

Ignore the factor 3.

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 '(-10m + 2mn + 4m2 + -5n)' equal to zero and attempt to solve:

Simplifying
-10m + 2mn + 4m2 + -5n = 0

Solving
-10m + 2mn + 4m2 + -5n = 0

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

Add '10m' to each side of the equation.
-10m + 2mn + 4m2 + 10m + -5n = 0 + 10m

Reorder the terms:
-10m + 10m + 2mn + 4m2 + -5n = 0 + 10m

Combine like terms: -10m + 10m = 0
0 + 2mn + 4m2 + -5n = 0 + 10m
2mn + 4m2 + -5n = 0 + 10m
Remove the zero:
2mn + 4m2 + -5n = 10m

Add '-2mn' to each side of the equation.
2mn + 4m2 + -2mn + -5n = 10m + -2mn

Reorder the terms:
2mn + -2mn + 4m2 + -5n = 10m + -2mn

Combine like terms: 2mn + -2mn = 0
0 + 4m2 + -5n = 10m + -2mn
4m2 + -5n = 10m + -2mn

Add '-4m2' to each side of the equation.
4m2 + -4m2 + -5n = 10m + -2mn + -4m2

Combine like terms: 4m2 + -4m2 = 0
0 + -5n = 10m + -2mn + -4m2
-5n = 10m + -2mn + -4m2

Add '5n' to each side of the equation.
-5n + 5n = 10m + -2mn + -4m2 + 5n

Combine like terms: -5n + 5n = 0
0 = 10m + -2mn + -4m2 + 5n

Simplifying
0 = 10m + -2mn + -4m2 + 5n

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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