a^2-5a-20=30

Solution for a^2-5a-20=30 equation:

Simplifying
a2 + -5a + -20 = 30

Reorder the terms:
-20 + -5a + a2 = 30

Solving
-20 + -5a + a2 = 30

Solving for variable 'a'.

Reorder the terms:
-20 + -30 + -5a + a2 = 30 + -30

Combine like terms: -20 + -30 = -50
-50 + -5a + a2 = 30 + -30

Combine like terms: 30 + -30 = 0
-50 + -5a + a2 = 0

Factor a trinomial.
(-5 + -1a)(10 + -1a) = 0

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

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 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 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
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
Solution
a = {-5, 10}