a^4+8a^3b-9a^2b^2=

Solution for a^4+8a^3b-9a^2b^2= equation:

Simplifying
a4 + 8a3b + -9a2b2 = 0

Reorder the terms:
-9a2b2 + 8a3b + a4 = 0

Solving
-9a2b2 + 8a3b + a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(-9b2 + 8ab + a2) = 0

Factor a trinomial.
a2((-9b + -1a)(b + -1a)) = 0

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 '(-9b + -1a)' equal to zero and attempt to solve:

Simplifying
-9b + -1a = 0

Reorder the terms:
-1a + -9b = 0

Solving
-1a + -9b = 0

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

Add '9b' to each side of the equation.
-1a + -9b + 9b = 0 + 9b

Combine like terms: -9b + 9b = 0
-1a + 0 = 0 + 9b
-1a = 0 + 9b
Remove the zero:
-1a = 9b

Divide each side by '-1'.
a = -9b

Simplifying
a = -9b
Subproblem 3
Set the factor '(b + -1a)' equal to zero and attempt to solve:

Simplifying
b + -1a = 0

Reorder the terms:
-1a + b = 0

Solving
-1a + b = 0

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

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

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

Divide each side by '-1'.
a = b

Simplifying
a = b
Solution
a = {0, -9b, b}