12p^2-78p+108=0

Solution for 12p^2-78p+108=0 equation:

Simplifying
12p2 + -78p + 108 = 0

Reorder the terms:
108 + -78p + 12p2 = 0

Solving
108 + -78p + 12p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + -13p + 2p2) = 0

Factor a trinomial.
6((2 + -1p)(9 + -2p)) = 0

Ignore the factor 6.
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 '(9 + -2p)' equal to zero and attempt to solve:

Simplifying
9 + -2p = 0

Solving
9 + -2p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2p = 0 + -9
-2p = 0 + -9

Combine like terms: 0 + -9 = -9
-2p = -9

Divide each side by '-2'.
p = 4.5

Simplifying
p = 4.5
Solution
p = {2, 4.5}