(8a+-1)(a+-1)=0

Solution for (8a+-1)(a+-1)=0 equation:

Simplifying
(8a + -1)(a + -1) = 0

Reorder the terms:
(-1 + 8a)(a + -1) = 0

Reorder the terms:
(-1 + 8a)(-1 + a) = 0

Multiply (-1 + 8a) * (-1 + a)
(-1(-1 + a) + 8a * (-1 + a)) = 0
((-1 * -1 + a * -1) + 8a * (-1 + a)) = 0
((1 + -1a) + 8a * (-1 + a)) = 0
(1 + -1a + (-1 * 8a + a * 8a)) = 0
(1 + -1a + (-8a + 8a2)) = 0

Combine like terms: -1a + -8a = -9a
(1 + -9a + 8a2) = 0

Solving
1 + -9a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -8a)(1 + -1a) = 0

Subproblem 1
Set the factor '(1 + -8a)' equal to zero and attempt to solve:

Simplifying
1 + -8a = 0

Solving
1 + -8a = 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 + -8a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8a = 0 + -1
-8a = 0 + -1

Combine like terms: 0 + -1 = -1
-8a = -1

Divide each side by '-8'.
a = 0.125

Simplifying
a = 0.125
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {0.125, 1}