6p^2+12p-81=0

Solution for 6p^2+12p-81=0 equation:

Simplifying
6p2 + 12p + -81 = 0

Reorder the terms:
-81 + 12p + 6p2 = 0

Solving
-81 + 12p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-27 + 4p + 2p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-27 + 4p + 2p2)' equal to zero and attempt to solve:

Simplifying
-27 + 4p + 2p2 = 0

Solving
-27 + 4p + 2p2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-13.5 + 2p + p2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 2p + 13.5 + p2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 2p + p2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 2p + p2 = 0 + 13.5
2p + p2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
2p + p2 = 13.5

The p term is 2p.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2p + 1 + p2 = 13.5 + 1

Reorder the terms:
1 + 2p + p2 = 13.5 + 1

Combine like terms: 13.5 + 1 = 14.5
1 + 2p + p2 = 14.5

Factor a perfect square on the left side:
(p + 1)(p + 1) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(p + 1) equal to 3.807886553 and -3.807886553.

Subproblem 1
p + 1 = 3.807886553

Simplifying
p + 1 = 3.807886553

Reorder the terms:
1 + p = 3.807886553

Solving
1 + p = 3.807886553

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = 3.807886553 + -1

Combine like terms: 1 + -1 = 0
0 + p = 3.807886553 + -1
p = 3.807886553 + -1

Combine like terms: 3.807886553 + -1 = 2.807886553
p = 2.807886553

Simplifying
p = 2.807886553

Subproblem 2
p + 1 = -3.807886553

Simplifying
p + 1 = -3.807886553

Reorder the terms:
1 + p = -3.807886553

Solving
1 + p = -3.807886553

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = -3.807886553 + -1

Combine like terms: 1 + -1 = 0
0 + p = -3.807886553 + -1
p = -3.807886553 + -1

Combine like terms: -3.807886553 + -1 = -4.807886553
p = -4.807886553

Simplifying
p = -4.807886553

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.807886553, -4.807886553}
Solution
p = {2.807886553, -4.807886553}