p(r^2+8r+16)=100p

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

Simplifying
p(r2 + 8r + 16) = 100p

Reorder the terms:
p(16 + 8r + r2) = 100p
(16 * p + 8r * p + r2 * p) = 100p
(16p + 8pr + pr2) = 100p

Solving
16p + 8pr + pr2 = 100p

Solving for variable 'p'.

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

Add '-100p' to each side of the equation.
16p + 8pr + -100p + pr2 = 100p + -100p

Reorder the terms:
16p + -100p + 8pr + pr2 = 100p + -100p

Combine like terms: 16p + -100p = -84p
-84p + 8pr + pr2 = 100p + -100p

Combine like terms: 100p + -100p = 0
-84p + 8pr + pr2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(-84 + 8r + r2) = 0

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

Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(-14 + -1r)' equal to zero and attempt to solve:

Simplifying
-14 + -1r = 0

Solving
-14 + -1r = 0

Move all terms containing p 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

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

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

Simplifying
0 = 14 + r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

Move all terms containing p 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

Add 'r' to each side of the equation.
-1r + r = -6 + r

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

Simplifying
0 = -6 + r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}