9p^2-54p+72=0

Solution for 9p^2-54p+72=0 equation:

Simplifying
9p2 + -54p + 72 = 0

Reorder the terms:
72 + -54p + 9p2 = 0

Solving
72 + -54p + 9p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '9'.
9(8 + -6p + p2) = 0

Factor a trinomial.
9((2 + -1p)(4 + -1p)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
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 = {2, 4}