16(p-1)=p(p+8)

Solution for 16(p-1)=p(p+8) equation:

Simplifying
16(p + -1) = p(p + 8)

Reorder the terms:
16(-1 + p) = p(p + 8)
(-1 * 16 + p * 16) = p(p + 8)
(-16 + 16p) = p(p + 8)

Reorder the terms:
-16 + 16p = p(8 + p)
-16 + 16p = (8 * p + p * p)
-16 + 16p = (8p + p2)

Solving
-16 + 16p = 8p + p2

Solving for variable 'p'.

Combine like terms: 16p + -8p = 8p
-16 + 8p + -1p2 = 8p + p2 + -8p + -1p2

Reorder the terms:
-16 + 8p + -1p2 = 8p + -8p + p2 + -1p2

Combine like terms: 8p + -8p = 0
-16 + 8p + -1p2 = 0 + p2 + -1p2
-16 + 8p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
-16 + 8p + -1p2 = 0

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

Subproblem 1
Set the factor '(-4 + p)' equal to zero and attempt to solve:

Simplifying
-4 + p = 0

Solving
-4 + p = 0

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

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

Combine like terms: -4 + 4 = 0
0 + p = 0 + 4
p = 0 + 4

Combine like terms: 0 + 4 = 4
p = 4

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

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

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

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

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

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

Simplifying
p = 4
Solution
p = {4, 4}