20a^2-144a-45=0

Solution for 20a^2-144a-45=0 equation:

Simplifying
20a2 + -144a + -45 = 0

Reorder the terms:
-45 + -144a + 20a2 = 0

Solving
-45 + -144a + 20a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -10a)(15 + -2a) = 0

Subproblem 1
Set the factor '(-3 + -10a)' equal to zero and attempt to solve:

Simplifying
-3 + -10a = 0

Solving
-3 + -10a = 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 + -10a = 0 + 3

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

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

Divide each side by '-10'.
a = -0.3

Simplifying
a = -0.3
Subproblem 2
Set the factor '(15 + -2a)' equal to zero and attempt to solve:

Simplifying
15 + -2a = 0

Solving
15 + -2a = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2a = 0 + -15
-2a = 0 + -15

Combine like terms: 0 + -15 = -15
-2a = -15

Divide each side by '-2'.
a = 7.5

Simplifying
a = 7.5
Solution
a = {-0.3, 7.5}