(4a+12)(5a-20)=0

Solution for (4a+12)(5a-20)=0 equation:

Simplifying
(4a + 12)(5a + -20) = 0

Reorder the terms:
(12 + 4a)(5a + -20) = 0

Reorder the terms:
(12 + 4a)(-20 + 5a) = 0

Multiply (12 + 4a) * (-20 + 5a)
(12(-20 + 5a) + 4a * (-20 + 5a)) = 0
((-20 * 12 + 5a * 12) + 4a * (-20 + 5a)) = 0
((-240 + 60a) + 4a * (-20 + 5a)) = 0
(-240 + 60a + (-20 * 4a + 5a * 4a)) = 0
(-240 + 60a + (-80a + 20a2)) = 0

Combine like terms: 60a + -80a = -20a
(-240 + -20a + 20a2) = 0

Solving
-240 + -20a + 20a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-12 + -1a + a2) = 0

Factor a trinomial.
20((-3 + -1a)(4 + -1a)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
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 = {-3, 4}