10a^2-10a-20=0

Solution for 10a^2-10a-20=0 equation:

Simplifying
10a2 + -10a + -20 = 0

Reorder the terms:
-20 + -10a + 10a2 = 0

Solving
-20 + -10a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-2 + -1a + a2) = 0

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

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
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
Solution
a = {-1, 2}