6p^2+12p-94=0

Solution for 6p^2+12p-94=0 equation:

Simplifying
6p2 + 12p + -94 = 0

Reorder the terms:
-94 + 12p + 6p2 = 0

Solving
-94 + 12p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-47 + 6p + 3p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-47 + 6p + 3p2)' equal to zero and attempt to solve:

Simplifying
-47 + 6p + 3p2 = 0

Solving
-47 + 6p + 3p2 = 0

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

Divide each side by '3'.
-15.66666667 + 2p + p2 = 0

Move the constant term to the right:

Add '15.66666667' to each side of the equation.
-15.66666667 + 2p + 15.66666667 + p2 = 0 + 15.66666667

Reorder the terms:
-15.66666667 + 15.66666667 + 2p + p2 = 0 + 15.66666667

Combine like terms: -15.66666667 + 15.66666667 = 0.00000000
0.00000000 + 2p + p2 = 0 + 15.66666667
2p + p2 = 0 + 15.66666667

Combine like terms: 0 + 15.66666667 = 15.66666667
2p + p2 = 15.66666667

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 = 15.66666667 + 1

Reorder the terms:
1 + 2p + p2 = 15.66666667 + 1

Combine like terms: 15.66666667 + 1 = 16.66666667
1 + 2p + p2 = 16.66666667

Factor a perfect square on the left side:
(p + 1)(p + 1) = 16.66666667

Calculate the square root of the right side: 4.082482905

Break this problem into two subproblems by setting 
(p + 1) equal to 4.082482905 and -4.082482905.

Subproblem 1
p + 1 = 4.082482905

Simplifying
p + 1 = 4.082482905

Reorder the terms:
1 + p = 4.082482905

Solving
1 + p = 4.082482905

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 = 4.082482905 + -1

Combine like terms: 1 + -1 = 0
0 + p = 4.082482905 + -1
p = 4.082482905 + -1

Combine like terms: 4.082482905 + -1 = 3.082482905
p = 3.082482905

Simplifying
p = 3.082482905

Subproblem 2
p + 1 = -4.082482905

Simplifying
p + 1 = -4.082482905

Reorder the terms:
1 + p = -4.082482905

Solving
1 + p = -4.082482905

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 = -4.082482905 + -1

Combine like terms: 1 + -1 = 0
0 + p = -4.082482905 + -1
p = -4.082482905 + -1

Combine like terms: -4.082482905 + -1 = -5.082482905
p = -5.082482905

Simplifying
p = -5.082482905

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.082482905, -5.082482905}
Solution
p = {3.082482905, -5.082482905}