6p^2-54p+108=0

Solution for 6p^2-54p+108=0 equation:

Simplifying
6p2 + -54p + 108 = 0

Reorder the terms:
108 + -54p + 6p2 = 0

Solving
108 + -54p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + -9p + p2) = 0

Factor a trinomial.
6((3 + -1p)(6 + -1p)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 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 + -1p = 0 + -6

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

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

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

Simplifying
p = 6
Solution
p = {3, 6}