4a^2b+95ab-25b=0

Solution for 4a^2b+95ab-25b=0 equation:

Simplifying
4a2b + 95ab + -25b = 0

Reorder the terms:
95ab + 4a2b + -25b = 0

Solving
95ab + 4a2b + -25b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(95a + 4a2 + -25) = 0

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

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

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 '(95a + 4a2 + -25)' equal to zero and attempt to solve:

Simplifying
95a + 4a2 + -25 = 0

Reorder the terms:
-25 + 95a + 4a2 = 0

Solving
-25 + 95a + 4a2 = 0

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

Divide each side by '4'.
-6.25 + 23.75a + a2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 23.75a + 6.25 + a2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 23.75a + a2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 23.75a + a2 = 0 + 6.25
23.75a + a2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
23.75a + a2 = 6.25

The a term is 23.75a.  Take half its coefficient (11.875).
Square it (141.015625) and add it to both sides.

Add '141.015625' to each side of the equation.
23.75a + 141.015625 + a2 = 6.25 + 141.015625

Reorder the terms:
141.015625 + 23.75a + a2 = 6.25 + 141.015625

Combine like terms: 6.25 + 141.015625 = 147.265625
141.015625 + 23.75a + a2 = 147.265625

Factor a perfect square on the left side:
(a + 11.875)(a + 11.875) = 147.265625

Calculate the square root of the right side: 12.135304899

Break this problem into two subproblems by setting 
(a + 11.875) equal to 12.135304899 and -12.135304899.

Subproblem 1
a + 11.875 = 12.135304899

Simplifying
a + 11.875 = 12.135304899

Reorder the terms:
11.875 + a = 12.135304899

Solving
11.875 + a = 12.135304899

Solving for variable 'a'.

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

Add '-11.875' to each side of the equation.
11.875 + -11.875 + a = 12.135304899 + -11.875

Combine like terms: 11.875 + -11.875 = 0.000
0.000 + a = 12.135304899 + -11.875
a = 12.135304899 + -11.875

Combine like terms: 12.135304899 + -11.875 = 0.260304899
a = 0.260304899

Simplifying
a = 0.260304899

Subproblem 2
a + 11.875 = -12.135304899

Simplifying
a + 11.875 = -12.135304899

Reorder the terms:
11.875 + a = -12.135304899

Solving
11.875 + a = -12.135304899

Solving for variable 'a'.

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

Add '-11.875' to each side of the equation.
11.875 + -11.875 + a = -12.135304899 + -11.875

Combine like terms: 11.875 + -11.875 = 0.000
0.000 + a = -12.135304899 + -11.875
a = -12.135304899 + -11.875

Combine like terms: -12.135304899 + -11.875 = -24.010304899
a = -24.010304899

Simplifying
a = -24.010304899

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.260304899, -24.010304899}
Solution
a = {0.260304899, -24.010304899}