(4a+8)(5a-20)=0

Solution for (4a+8)(5a-20)=0 equation:

Simplifying
(4a + 8)(5a + -20) = 0

Reorder the terms:
(8 + 4a)(5a + -20) = 0

Reorder the terms:
(8 + 4a)(-20 + 5a) = 0

Multiply (8 + 4a) * (-20 + 5a)
(8(-20 + 5a) + 4a * (-20 + 5a)) = 0
((-20 * 8 + 5a * 8) + 4a * (-20 + 5a)) = 0
((-160 + 40a) + 4a * (-20 + 5a)) = 0
(-160 + 40a + (-20 * 4a + 5a * 4a)) = 0
(-160 + 40a + (-80a + 20a2)) = 0

Combine like terms: 40a + -80a = -40a
(-160 + -40a + 20a2) = 0

Solving
-160 + -40a + 20a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-8 + -2a + a2) = 0

Factor a trinomial.
20((-2 + -1a)(4 + -1a)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

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

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

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

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

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

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

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

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

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-2, 4}