(20a-20)(4a+6)=0

Solution for (20a-20)(4a+6)=0 equation:

Simplifying
(20a + -20)(4a + 6) = 0

Reorder the terms:
(-20 + 20a)(4a + 6) = 0

Reorder the terms:
(-20 + 20a)(6 + 4a) = 0

Multiply (-20 + 20a) * (6 + 4a)
(-20(6 + 4a) + 20a * (6 + 4a)) = 0
((6 * -20 + 4a * -20) + 20a * (6 + 4a)) = 0
((-120 + -80a) + 20a * (6 + 4a)) = 0
(-120 + -80a + (6 * 20a + 4a * 20a)) = 0
(-120 + -80a + (120a + 80a2)) = 0

Combine like terms: -80a + 120a = 40a
(-120 + 40a + 80a2) = 0

Solving
-120 + 40a + 80a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '40'.
40(-3 + a + 2a2) = 0

Factor a trinomial.
40((-3 + -2a)(1 + -1a)) = 0

Ignore the factor 40.
Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve:

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 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 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
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 = {-1.5, 1}