a^2-3a-45=-5

Solution for a^2-3a-45=-5 equation:

Simplifying
a2 + -3a + -45 = -5

Reorder the terms:
-45 + -3a + a2 = -5

Solving
-45 + -3a + a2 = -5

Solving for variable 'a'.

Reorder the terms:
-45 + 5 + -3a + a2 = -5 + 5

Combine like terms: -45 + 5 = -40
-40 + -3a + a2 = -5 + 5

Combine like terms: -5 + 5 = 0
-40 + -3a + a2 = 0

Factor a trinomial.
(-5 + -1a)(8 + -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 '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {-5, 8}