a^2-a-462=0

Solution for a^2-a-462=0 equation:

Simplifying
a2 + -1a + -462 = 0

Reorder the terms:
-462 + -1a + a2 = 0

Solving
-462 + -1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-21 + -1a)(22 + -1a) = 0

Subproblem 1
Set the factor '(-21 + -1a)' equal to zero and attempt to solve:

Simplifying
-21 + -1a = 0

Solving
-21 + -1a = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1a = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1a = 0 + 21
-1a = 0 + 21

Combine like terms: 0 + 21 = 21
-1a = 21

Divide each side by '-1'.
a = -21

Simplifying
a = -21
Subproblem 2
Set the factor '(22 + -1a)' equal to zero and attempt to solve:

Simplifying
22 + -1a = 0

Solving
22 + -1a = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1a = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1a = 0 + -22
-1a = 0 + -22

Combine like terms: 0 + -22 = -22
-1a = -22

Divide each side by '-1'.
a = 22

Simplifying
a = 22
Solution
a = {-21, 22}