3p^2+6p-7=0

Solution for 3p^2+6p-7=0 equation:

Simplifying
3p2 + 6p + -7 = 0

Reorder the terms:
-7 + 6p + 3p2 = 0

Solving
-7 + 6p + 3p2 = 0

Solving for variable 'p'.

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

Divide each side by '3'.
-2.333333333 + 2p + p2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 2p + 2.333333333 + p2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 2p + p2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 2p + p2 = 0 + 2.333333333
2p + p2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
2p + p2 = 2.333333333

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 = 2.333333333 + 1

Reorder the terms:
1 + 2p + p2 = 2.333333333 + 1

Combine like terms: 2.333333333 + 1 = 3.333333333
1 + 2p + p2 = 3.333333333

Factor a perfect square on the left side:
(p + 1)(p + 1) = 3.333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(p + 1) equal to 1.825741858 and -1.825741858.

Subproblem 1
p + 1 = 1.825741858

Simplifying
p + 1 = 1.825741858

Reorder the terms:
1 + p = 1.825741858

Solving
1 + p = 1.825741858

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 = 1.825741858 + -1

Combine like terms: 1 + -1 = 0
0 + p = 1.825741858 + -1
p = 1.825741858 + -1

Combine like terms: 1.825741858 + -1 = 0.825741858
p = 0.825741858

Simplifying
p = 0.825741858

Subproblem 2
p + 1 = -1.825741858

Simplifying
p + 1 = -1.825741858

Reorder the terms:
1 + p = -1.825741858

Solving
1 + p = -1.825741858

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 = -1.825741858 + -1

Combine like terms: 1 + -1 = 0
0 + p = -1.825741858 + -1
p = -1.825741858 + -1

Combine like terms: -1.825741858 + -1 = -2.825741858
p = -2.825741858

Simplifying
p = -2.825741858

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.825741858, -2.825741858}