5p*p+2p-6=0

Solution for 5p*p+2p-6=0 equation:

Simplifying
5p * p + 2p + -6 = 0

Multiply p * p
5p2 + 2p + -6 = 0

Reorder the terms:
-6 + 2p + 5p2 = 0

Solving
-6 + 2p + 5p2 = 0

Solving for variable 'p'.

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

Divide each side by '5'.
-1.2 + 0.4p + p2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 0.4p + 1.2 + p2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 0.4p + p2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 0.4p + p2 = 0 + 1.2
0.4p + p2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
0.4p + p2 = 1.2

The p term is 0.4p.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4p + 0.04 + p2 = 1.2 + 0.04

Reorder the terms:
0.04 + 0.4p + p2 = 1.2 + 0.04

Combine like terms: 1.2 + 0.04 = 1.24
0.04 + 0.4p + p2 = 1.24

Factor a perfect square on the left side:
(p + 0.2)(p + 0.2) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(p + 0.2) equal to 1.113552873 and -1.113552873.

Subproblem 1
p + 0.2 = 1.113552873

Simplifying
p + 0.2 = 1.113552873

Reorder the terms:
0.2 + p = 1.113552873

Solving
0.2 + p = 1.113552873

Solving for variable 'p'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + p = 1.113552873 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + p = 1.113552873 + -0.2
p = 1.113552873 + -0.2

Combine like terms: 1.113552873 + -0.2 = 0.913552873
p = 0.913552873

Simplifying
p = 0.913552873

Subproblem 2
p + 0.2 = -1.113552873

Simplifying
p + 0.2 = -1.113552873

Reorder the terms:
0.2 + p = -1.113552873

Solving
0.2 + p = -1.113552873

Solving for variable 'p'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + p = -1.113552873 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + p = -1.113552873 + -0.2
p = -1.113552873 + -0.2

Combine like terms: -1.113552873 + -0.2 = -1.313552873
p = -1.313552873

Simplifying
p = -1.313552873

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.913552873, -1.313552873}