36a^3b^2+66a^2b^3-210ab^4=0

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Solution for 36a^3b^2+66a^2b^3-210ab^4=0 equation: 


Simplifying
36a3b2 + 66a2b3 + -210ab4 = 0

Reorder the terms:
-210ab4 + 66a2b3 + 36a3b2 = 0

Solving
-210ab4 + 66a2b3 + 36a3b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6ab2'.
6ab2(-35b2 + 11ab + 6a2) = 0

Factor a trinomial.
6ab2((-7b + -2a)(5b + -3a)) = 0

Ignore the factor 6.

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 '(-7b + -2a)' equal to zero and attempt to solve:

Simplifying
-7b + -2a = 0

Reorder the terms:
-2a + -7b = 0

Solving
-2a + -7b = 0

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

Add '7b' to each side of the equation.
-2a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
-2a + 0 = 0 + 7b
-2a = 0 + 7b
Remove the zero:
-2a = 7b

Divide each side by '-2'.
a = -3.5b

Simplifying
a = -3.5b

Subproblem 3
Set the factor '(5b + -3a)' equal to zero and attempt to solve:

Simplifying
5b + -3a = 0

Reorder the terms:
-3a + 5b = 0

Solving
-3a + 5b = 0

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

Add '-5b' to each side of the equation.
-3a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
-3a + 0 = 0 + -5b
-3a = 0 + -5b
Remove the zero:
-3a = -5b

Divide each side by '-3'.
a = 1.666666667b

Simplifying
a = 1.666666667b
Solution
a = {-3.5b, 1.666666667b}

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