a^2-21a-46=0

Solution for a^2-21a-46=0 equation:

Simplifying
a2 + -21a + -46 = 0

Reorder the terms:
-46 + -21a + a2 = 0

Solving
-46 + -21a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -1a)(23 + -1a) = 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 '(23 + -1a)' equal to zero and attempt to solve:

Simplifying
23 + -1a = 0

Solving
23 + -1a = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1a = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1a = 0 + -23
-1a = 0 + -23

Combine like terms: 0 + -23 = -23
-1a = -23

Divide each side by '-1'.
a = 23

Simplifying
a = 23
Solution
a = {-2, 23}