r^2+14r+45=-3

Solution for r^2+14r+45=-3 equation:

Simplifying
r2 + 14r + 45 = -3

Reorder the terms:
45 + 14r + r2 = -3

Solving
45 + 14r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
45 + 3 + 14r + r2 = -3 + 3

Combine like terms: 45 + 3 = 48
48 + 14r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
48 + 14r + r2 = 0

Factor a trinomial.
(8 + r)(6 + r) = 0

Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve:

Simplifying
8 + r = 0

Solving
8 + r = 0

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

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

Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8

Combine like terms: 0 + -8 = -8
r = -8

Simplifying
r = -8
Subproblem 2
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {-8, -6}