a^5+7ab^4-8a^3b^2=0

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Solution for a^5+7ab^4-8a^3b^2=0 equation: 


Simplifying
a5 + 7ab4 + -8a3b2 = 0

Reorder the terms:
7ab4 + -8a3b2 + a5 = 0

Solving
7ab4 + -8a3b2 + a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(7b4 + -8a2b2 + a4) = 0

Factor a trinomial.
a((b2 + -1a2)(7b2 + -1a2)) = 0

Factor a difference between two squares.
a(((b + a)(b + -1a))(7b2 + -1a2)) = 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 '(7b2 + -1a2)' equal to zero and attempt to solve:

Simplifying
7b2 + -1a2 = 0

Reorder the terms:
-1a2 + 7b2 = 0

Solving
-1a2 + 7b2 = 0

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

Add '-7b2' to each side of the equation.
-1a2 + 7b2 + -7b2 = 0 + -7b2

Combine like terms: 7b2 + -7b2 = 0
-1a2 + 0 = 0 + -7b2
-1a2 = 0 + -7b2
Remove the zero:
-1a2 = -7b2

Divide each side by '-1'.
a2 = 7b2

Simplifying
a2 = 7b2

Take the square root of each side:
a = {-2.645751311b, 2.645751311b}

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

Simplifying
b + a = 0

Reorder the terms:
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b

Subproblem 4
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, -2.645751311b, 2.645751311b, -1b, b}

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