a^2-14a-37=-5

Solution for a^2-14a-37=-5 equation:

Simplifying
a2 + -14a + -37 = -5

Reorder the terms:
-37 + -14a + a2 = -5

Solving
-37 + -14a + a2 = -5

Solving for variable 'a'.

Reorder the terms:
-37 + 5 + -14a + a2 = -5 + 5

Combine like terms: -37 + 5 = -32
-32 + -14a + a2 = -5 + 5

Combine like terms: -5 + 5 = 0
-32 + -14a + a2 = 0

Factor a trinomial.
(-2 + -1a)(16 + -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 '(16 + -1a)' equal to zero and attempt to solve:

Simplifying
16 + -1a = 0

Solving
16 + -1a = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1a = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1a = 0 + -16
-1a = 0 + -16

Combine like terms: 0 + -16 = -16
-1a = -16

Divide each side by '-1'.
a = 16

Simplifying
a = 16
Solution
a = {-2, 16}