20a^2-7a-40=0

Solution for 20a^2-7a-40=0 equation:

Simplifying
20a2 + -7a + -40 = 0

Reorder the terms:
-40 + -7a + 20a2 = 0

Solving
-40 + -7a + 20a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -4a)(8 + -5a) = 0

Subproblem 1
Set the factor '(-5 + -4a)' equal to zero and attempt to solve:

Simplifying
-5 + -4a = 0

Solving
-5 + -4a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4a = 0 + 5
-4a = 0 + 5

Combine like terms: 0 + 5 = 5
-4a = 5

Divide each side by '-4'.
a = -1.25

Simplifying
a = -1.25
Subproblem 2
Set the factor '(8 + -5a)' equal to zero and attempt to solve:

Simplifying
8 + -5a = 0

Solving
8 + -5a = 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 + -5a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5a = 0 + -8
-5a = 0 + -8

Combine like terms: 0 + -8 = -8
-5a = -8

Divide each side by '-5'.
a = 1.6

Simplifying
a = 1.6
Solution
a = {-1.25, 1.6}