r^2+16r-83=-3

Solution for r^2+16r-83=-3 equation:

Simplifying
r2 + 16r + -83 = -3

Reorder the terms:
-83 + 16r + r2 = -3

Solving
-83 + 16r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
-83 + 3 + 16r + r2 = -3 + 3

Combine like terms: -83 + 3 = -80
-80 + 16r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
-80 + 16r + r2 = 0

Factor a trinomial.
(-20 + -1r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-20 + -1r)' equal to zero and attempt to solve:

Simplifying
-20 + -1r = 0

Solving
-20 + -1r = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1r = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1r = 0 + 20
-1r = 0 + 20

Combine like terms: 0 + 20 = 20
-1r = 20

Divide each side by '-1'.
r = -20

Simplifying
r = -20
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {-20, 4}