42a^2b+95ab+25b=

Solution for 42a^2b+95ab+25b= equation:

Simplifying
42a2b + 95ab + 25b = 0

Reorder the terms:
95ab + 42a2b + 25b = 0

Solving
95ab + 42a2b + 25b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(95a + 42a2 + 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 + 42a2 + 25)' equal to zero and attempt to solve:

Simplifying
95a + 42a2 + 25 = 0

Reorder the terms:
25 + 95a + 42a2 = 0

Solving
25 + 95a + 42a2 = 0

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

Divide each side by '42'.
0.5952380952 + 2.261904762a + a2 = 0

Move the constant term to the right:

Add '-0.5952380952' to each side of the equation.
0.5952380952 + 2.261904762a + -0.5952380952 + a2 = 0 + -0.5952380952

Reorder the terms:
0.5952380952 + -0.5952380952 + 2.261904762a + a2 = 0 + -0.5952380952

Combine like terms: 0.5952380952 + -0.5952380952 = 0.0000000000
0.0000000000 + 2.261904762a + a2 = 0 + -0.5952380952
2.261904762a + a2 = 0 + -0.5952380952

Combine like terms: 0 + -0.5952380952 = -0.5952380952
2.261904762a + a2 = -0.5952380952

The a term is 2.261904762a.  Take half its coefficient (1.130952381).
Square it (1.279053288) and add it to both sides.

Add '1.279053288' to each side of the equation.
2.261904762a + 1.279053288 + a2 = -0.5952380952 + 1.279053288

Reorder the terms:
1.279053288 + 2.261904762a + a2 = -0.5952380952 + 1.279053288

Combine like terms: -0.5952380952 + 1.279053288 = 0.6838151928
1.279053288 + 2.261904762a + a2 = 0.6838151928

Factor a perfect square on the left side:
(a + 1.130952381)(a + 1.130952381) = 0.6838151928

Calculate the square root of the right side: 0.82693119

Break this problem into two subproblems by setting 
(a + 1.130952381) equal to 0.82693119 and -0.82693119.

Subproblem 1
a + 1.130952381 = 0.82693119

Simplifying
a + 1.130952381 = 0.82693119

Reorder the terms:
1.130952381 + a = 0.82693119

Solving
1.130952381 + a = 0.82693119

Solving for variable 'a'.

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

Add '-1.130952381' to each side of the equation.
1.130952381 + -1.130952381 + a = 0.82693119 + -1.130952381

Combine like terms: 1.130952381 + -1.130952381 = 0.000000000
0.000000000 + a = 0.82693119 + -1.130952381
a = 0.82693119 + -1.130952381

Combine like terms: 0.82693119 + -1.130952381 = -0.304021191
a = -0.304021191

Simplifying
a = -0.304021191

Subproblem 2
a + 1.130952381 = -0.82693119

Simplifying
a + 1.130952381 = -0.82693119

Reorder the terms:
1.130952381 + a = -0.82693119

Solving
1.130952381 + a = -0.82693119

Solving for variable 'a'.

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

Add '-1.130952381' to each side of the equation.
1.130952381 + -1.130952381 + a = -0.82693119 + -1.130952381

Combine like terms: 1.130952381 + -1.130952381 = 0.000000000
0.000000000 + a = -0.82693119 + -1.130952381
a = -0.82693119 + -1.130952381

Combine like terms: -0.82693119 + -1.130952381 = -1.957883571
a = -1.957883571

Simplifying
a = -1.957883571

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.304021191, -1.957883571}
Solution
a = {-0.304021191, -1.957883571}