50a^2b^5-35a^4b^3+5a^3b^4=0

Solution for 50a^2b^5-35a^4b^3+5a^3b^4=0 equation:

Simplifying
50a2b5 + -35a4b3 + 5a3b4 = 0

Reorder the terms:
50a2b5 + 5a3b4 + -35a4b3 = 0

Solving
50a2b5 + 5a3b4 + -35a4b3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2b3'.
5a2b3(10b2 + ab + -7a2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'a2b3' equal to zero and attempt to solve:

Simplifying
a2b3 = 0

Solving
a2b3 = 0

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

Simplifying
a2b3 = 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 '(10b2 + ab + -7a2)' equal to zero and attempt to solve:

Simplifying
10b2 + ab + -7a2 = 0

Reorder the terms:
ab + -7a2 + 10b2 = 0

Solving
ab + -7a2 + 10b2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.1428571429ab + a2 + -1.428571429b2 = 0

Move the constant term to the right:

Add '1.428571429b2' to each side of the equation.
-0.1428571429ab + a2 + -1.428571429b2 + 1.428571429b2 = 0 + 1.428571429b2

Combine like terms: -1.428571429b2 + 1.428571429b2 = 0.000000000
-0.1428571429ab + a2 + 0.000000000 = 0 + 1.428571429b2
-0.1428571429ab + a2 = 0 + 1.428571429b2
Remove the zero:
-0.1428571429ab + a2 = 1.428571429b2

The a term is ab.  Take half its coefficient (0.5b).
Square it (0.25b2) and add it to both sides.

Add '0.25b2' to each side of the equation.
-0.1428571429ab + a2 + 0.25b2 = 1.428571429b2 + 0.25b2

Combine like terms: 1.428571429b2 + 0.25b2 = 1.678571429b2
-0.1428571429ab + a2 + 0.25b2 = 1.678571429b2

Factor a perfect square on the left side:
(a + 0.5b)(a + 0.5b) = 1.678571429b2

Calculate the square root of the right side: 1.295596939b

Break this problem into two subproblems by setting 
(a + 0.5b) equal to 1.295596939b and -1.295596939b.

Subproblem 1
a + 0.5b = 1.295596939b

Simplifying
a + 0.5b = 1.295596939b

Solving
a + 0.5b = 1.295596939b

Solving for variable 'a'.

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

Add '-0.5b' to each side of the equation.
a + 0.5b + -0.5b = 1.295596939b + -0.5b

Combine like terms: 0.5b + -0.5b = 0.0
a + 0.0 = 1.295596939b + -0.5b
a = 1.295596939b + -0.5b

Combine like terms: 1.295596939b + -0.5b = 0.795596939b
a = 0.795596939b

Simplifying
a = 0.795596939b

Subproblem 2
a + 0.5b = -1.295596939b

Simplifying
a + 0.5b = -1.295596939b

Solving
a + 0.5b = -1.295596939b

Solving for variable 'a'.

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

Add '-0.5b' to each side of the equation.
a + 0.5b + -0.5b = -1.295596939b + -0.5b

Combine like terms: 0.5b + -0.5b = 0.0
a + 0.0 = -1.295596939b + -0.5b
a = -1.295596939b + -0.5b

Combine like terms: -1.295596939b + -0.5b = -1.795596939b
a = -1.795596939b

Simplifying
a = -1.795596939b

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.795596939b, -1.795596939b}
Solution
a = {0.795596939b, -1.795596939b}