5p^2+3*2p=2

Solution for 5p^2+3*2p=2 equation:

Simplifying
5p2 + 3 * 2p = 2

Multiply 3 * 2
5p2 + 6p = 2

Reorder the terms:
6p + 5p2 = 2

Solving
6p + 5p2 = 2

Solving for variable 'p'.

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

Combine like terms: 2 + -2 = 0
-2 + 6p + 5p2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The p term is 1.2p.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2p + 0.36 + p2 = 0.4 + 0.36

Reorder the terms:
0.36 + 1.2p + p2 = 0.4 + 0.36

Combine like terms: 0.4 + 0.36 = 0.76
0.36 + 1.2p + p2 = 0.76

Factor a perfect square on the left side:
(p + 0.6)(p + 0.6) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(p + 0.6) equal to 0.871779789 and -0.871779789.

Subproblem 1
p + 0.6 = 0.871779789

Simplifying
p + 0.6 = 0.871779789

Reorder the terms:
0.6 + p = 0.871779789

Solving
0.6 + p = 0.871779789

Solving for variable 'p'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + p = 0.871779789 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + p = 0.871779789 + -0.6
p = 0.871779789 + -0.6

Combine like terms: 0.871779789 + -0.6 = 0.271779789
p = 0.271779789

Simplifying
p = 0.271779789

Subproblem 2
p + 0.6 = -0.871779789

Simplifying
p + 0.6 = -0.871779789

Reorder the terms:
0.6 + p = -0.871779789

Solving
0.6 + p = -0.871779789

Solving for variable 'p'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + p = -0.871779789 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + p = -0.871779789 + -0.6
p = -0.871779789 + -0.6

Combine like terms: -0.871779789 + -0.6 = -1.471779789
p = -1.471779789

Simplifying
p = -1.471779789

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.271779789, -1.471779789}