24a^4+6a^3b-9a^2b^2=0

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Solution for 24a^4+6a^3b-9a^2b^2=0 equation: 


Simplifying
24a4 + 6a3b + -9a2b2 = 0

Reorder the terms:
-9a2b2 + 6a3b + 24a4 = 0

Solving
-9a2b2 + 6a3b + 24a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a2'.
3a2(-3b2 + 2ab + 8a2) = 0

Factor a trinomial.
3a2((-3b + -4a)(b + -2a)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}

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

Simplifying
-3b + -4a = 0

Reorder the terms:
-4a + -3b = 0

Solving
-4a + -3b = 0

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

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

Combine like terms: -3b + 3b = 0
-4a + 0 = 0 + 3b
-4a = 0 + 3b
Remove the zero:
-4a = 3b

Divide each side by '-4'.
a = -0.75b

Simplifying
a = -0.75b

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

Simplifying
b + -2a = 0

Reorder the terms:
-2a + b = 0

Solving
-2a + b = 0

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

Add '-1b' to each side of the equation.
-2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-2a + 0 = 0 + -1b
-2a = 0 + -1b
Remove the zero:
-2a = -1b

Divide each side by '-2'.
a = 0.5b

Simplifying
a = 0.5b
Solution
a = {0, -0.75b, 0.5b}

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