(4a+1)(a+8)=0

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

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

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

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

Multiply (1 + 4a) * (8 + a)
(1(8 + a) + 4a * (8 + a)) = 0
((8 * 1 + a * 1) + 4a * (8 + a)) = 0
((8 + 1a) + 4a * (8 + a)) = 0
(8 + 1a + (8 * 4a + a * 4a)) = 0
(8 + 1a + (32a + 4a2)) = 0

Combine like terms: 1a + 32a = 33a
(8 + 33a + 4a2) = 0

Solving
8 + 33a + 4a2 = 0

Solving for variable 'a'.

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

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

Simplifying
8 + a = 0

Solving
8 + a = 0

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

Add '-8' to each side of the equation.
8 + -8 + a = 0 + -8

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

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

Simplifying
a = -8
Subproblem 2
Set the factor '(1 + 4a)' equal to zero and attempt to solve:

Simplifying
1 + 4a = 0

Solving
1 + 4a = 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 + 4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4a = 0 + -1
4a = 0 + -1

Combine like terms: 0 + -1 = -1
4a = -1

Divide each side by '4'.
a = -0.25

Simplifying
a = -0.25
Solution
a = {-8, -0.25}