10a^2-100a-2000=0

Solution for 10a^2-100a-2000=0 equation:

Simplifying
10a2 + -100a + -2000 = 0

Reorder the terms:
-2000 + -100a + 10a2 = 0

Solving
-2000 + -100a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-200 + -10a + a2) = 0

Factor a trinomial.
10((-10 + -1a)(20 + -1a)) = 0

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

Simplifying
-10 + -1a = 0

Solving
-10 + -1a = 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 + -1a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1a = 0 + 10
-1a = 0 + 10

Combine like terms: 0 + 10 = 10
-1a = 10

Divide each side by '-1'.
a = -10

Simplifying
a = -10
Subproblem 2
Set the factor '(20 + -1a)' equal to zero and attempt to solve:

Simplifying
20 + -1a = 0

Solving
20 + -1a = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1a = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1a = 0 + -20
-1a = 0 + -20

Combine like terms: 0 + -20 = -20
-1a = -20

Divide each side by '-1'.
a = 20

Simplifying
a = 20
Solution
a = {-10, 20}