3a^2-4a-20=0

Solution for 3a^2-4a-20=0 equation:

Simplifying
3a2 + -4a + -20 = 0

Reorder the terms:
-20 + -4a + 3a2 = 0

Solving
-20 + -4a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -1a)(10 + -3a) = 0

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 '(10 + -3a)' equal to zero and attempt to solve:

Simplifying
10 + -3a = 0

Solving
10 + -3a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3a = 0 + -10
-3a = 0 + -10

Combine like terms: 0 + -10 = -10
-3a = -10

Divide each side by '-3'.
a = 3.333333333

Simplifying
a = 3.333333333
Solution
a = {-2, 3.333333333}