6p^2-12p-80=0

Solution for 6p^2-12p-80=0 equation:

Simplifying
6p2 + -12p + -80 = 0

Reorder the terms:
-80 + -12p + 6p2 = 0

Solving
-80 + -12p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -6p + 3p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-40 + -6p + 3p2)' equal to zero and attempt to solve:

Simplifying
-40 + -6p + 3p2 = 0

Solving
-40 + -6p + 3p2 = 0

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

Divide each side by '3'.
-13.33333333 + -2p + p2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -2p + 13.33333333 + p2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -2p + p2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -2p + p2 = 0 + 13.33333333
-2p + p2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-2p + p2 = 13.33333333

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 = 13.33333333 + 1

Reorder the terms:
1 + -2p + p2 = 13.33333333 + 1

Combine like terms: 13.33333333 + 1 = 14.33333333
1 + -2p + p2 = 14.33333333

Factor a perfect square on the left side:
(p + -1)(p + -1) = 14.33333333

Calculate the square root of the right side: 3.785938897

Break this problem into two subproblems by setting 
(p + -1) equal to 3.785938897 and -3.785938897.

Subproblem 1
p + -1 = 3.785938897

Simplifying
p + -1 = 3.785938897

Reorder the terms:
-1 + p = 3.785938897

Solving
-1 + p = 3.785938897

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 = 3.785938897 + 1

Combine like terms: -1 + 1 = 0
0 + p = 3.785938897 + 1
p = 3.785938897 + 1

Combine like terms: 3.785938897 + 1 = 4.785938897
p = 4.785938897

Simplifying
p = 4.785938897

Subproblem 2
p + -1 = -3.785938897

Simplifying
p + -1 = -3.785938897

Reorder the terms:
-1 + p = -3.785938897

Solving
-1 + p = -3.785938897

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 = -3.785938897 + 1

Combine like terms: -1 + 1 = 0
0 + p = -3.785938897 + 1
p = -3.785938897 + 1

Combine like terms: -3.785938897 + 1 = -2.785938897
p = -2.785938897

Simplifying
p = -2.785938897

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.785938897, -2.785938897}
Solution
p = {4.785938897, -2.785938897}