(-2a-1)(-4a-8)=0

Solution for (-2a-1)(-4a-8)=0 equation:

Simplifying
(-2a + -1)(-4a + -8) = 0

Reorder the terms:
(-1 + -2a)(-4a + -8) = 0

Reorder the terms:
(-1 + -2a)(-8 + -4a) = 0

Multiply (-1 + -2a) * (-8 + -4a)
(-1(-8 + -4a) + -2a * (-8 + -4a)) = 0
((-8 * -1 + -4a * -1) + -2a * (-8 + -4a)) = 0
((8 + 4a) + -2a * (-8 + -4a)) = 0
(8 + 4a + (-8 * -2a + -4a * -2a)) = 0
(8 + 4a + (16a + 8a2)) = 0

Combine like terms: 4a + 16a = 20a
(8 + 20a + 8a2) = 0

Solving
8 + 20a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 5a + 2a2) = 0

Factor a trinomial.
4((2 + a)(1 + 2a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

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

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

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

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

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

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

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

Simplifying
a = -0.5
Solution
a = {-2, -0.5}