r^2+8r+16=100

Solution for r^2+8r+16=100 equation:

Simplifying
r2 + 8r + 16 = 100

Reorder the terms:
16 + 8r + r2 = 100

Solving
16 + 8r + r2 = 100

Solving for variable 'r'.

Reorder the terms:
16 + -100 + 8r + r2 = 100 + -100

Combine like terms: 16 + -100 = -84
-84 + 8r + r2 = 100 + -100

Combine like terms: 100 + -100 = 0
-84 + 8r + r2 = 0

Factor a trinomial.
(-14 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-14 + -1r)' equal to zero and attempt to solve:

Simplifying
-14 + -1r = 0

Solving
-14 + -1r = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1r = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1r = 0 + 14
-1r = 0 + 14

Combine like terms: 0 + 14 = 14
-1r = 14

Divide each side by '-1'.
r = -14

Simplifying
r = -14
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 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 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-14, 6}