-a^2-29a+62=0

Solution for -a^2-29a+62=0 equation:

Simplifying
-1a2 + -29a + 62 = 0

Reorder the terms:
62 + -29a + -1a2 = 0

Solving
62 + -29a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a)(31 + a) = 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 '(31 + a)' equal to zero and attempt to solve:

Simplifying
31 + a = 0

Solving
31 + a = 0

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

Add '-31' to each side of the equation.
31 + -31 + a = 0 + -31

Combine like terms: 31 + -31 = 0
0 + a = 0 + -31
a = 0 + -31

Combine like terms: 0 + -31 = -31
a = -31

Simplifying
a = -31
Solution
a = {2, -31}