1-8ab-20a^2b^2=0

Solution for 1-8ab-20a^2b^2=0 equation:

Simplifying
1 + -8ab + -20a2b2 = 0

Solving
1 + -8ab + -20a2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -10ab)(1 + 2ab) = 0

Subproblem 1
Set the factor '(1 + -10ab)' equal to zero and attempt to solve:

Simplifying
1 + -10ab = 0

Solving
1 + -10ab = 0

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

Add '-1' to each side of the equation.
1 + -1 + -10ab = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10ab = 0 + -1
-10ab = 0 + -1

Combine like terms: 0 + -1 = -1
-10ab = -1

Divide each side by '-10b'.
a = 0.1b-1

Simplifying
a = 0.1b-1
Subproblem 2
Set the factor '(1 + 2ab)' equal to zero and attempt to solve:

Simplifying
1 + 2ab = 0

Solving
1 + 2ab = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2ab = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2ab = 0 + -1
2ab = 0 + -1

Combine like terms: 0 + -1 = -1
2ab = -1

Divide each side by '2b'.
a = -0.5b-1

Simplifying
a = -0.5b-1
Solution
a = {0.1b-1, -0.5b-1}