(5p+3)(5p+3)=8

Solution for (5p+3)(5p+3)=8 equation:

Simplifying
(5p + 3)(5p + 3) = 8

Reorder the terms:
(3 + 5p)(5p + 3) = 8

Reorder the terms:
(3 + 5p)(3 + 5p) = 8

Multiply (3 + 5p) * (3 + 5p)
(3(3 + 5p) + 5p * (3 + 5p)) = 8
((3 * 3 + 5p * 3) + 5p * (3 + 5p)) = 8
((9 + 15p) + 5p * (3 + 5p)) = 8
(9 + 15p + (3 * 5p + 5p * 5p)) = 8
(9 + 15p + (15p + 25p2)) = 8

Combine like terms: 15p + 15p = 30p
(9 + 30p + 25p2) = 8

Solving
9 + 30p + 25p2 = 8

Solving for variable 'p'.

Reorder the terms:
9 + -8 + 30p + 25p2 = 8 + -8

Combine like terms: 9 + -8 = 1
1 + 30p + 25p2 = 8 + -8

Combine like terms: 8 + -8 = 0
1 + 30p + 25p2 = 0

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

Divide each side by '25'.
0.04 + 1.2p + p2 = 0

Move the constant term to the right:

Add '-0.04' to each side of the equation.
0.04 + 1.2p + -0.04 + p2 = 0 + -0.04

Reorder the terms:
0.04 + -0.04 + 1.2p + p2 = 0 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
0.00 + 1.2p + p2 = 0 + -0.04
1.2p + p2 = 0 + -0.04

Combine like terms: 0 + -0.04 = -0.04
1.2p + p2 = -0.04

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 = -0.04 + 0.36

Reorder the terms:
0.36 + 1.2p + p2 = -0.04 + 0.36

Combine like terms: -0.04 + 0.36 = 0.32
0.36 + 1.2p + p2 = 0.32

Factor a perfect square on the left side:
(p + 0.6)(p + 0.6) = 0.32

Calculate the square root of the right side: 0.565685425

Break this problem into two subproblems by setting 
(p + 0.6) equal to 0.565685425 and -0.565685425.

Subproblem 1
p + 0.6 = 0.565685425

Simplifying
p + 0.6 = 0.565685425

Reorder the terms:
0.6 + p = 0.565685425

Solving
0.6 + p = 0.565685425

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 = 0.565685425 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + p = 0.565685425 + -0.6
p = 0.565685425 + -0.6

Combine like terms: 0.565685425 + -0.6 = -0.034314575
p = -0.034314575

Simplifying
p = -0.034314575

Subproblem 2
p + 0.6 = -0.565685425

Simplifying
p + 0.6 = -0.565685425

Reorder the terms:
0.6 + p = -0.565685425

Solving
0.6 + p = -0.565685425

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 = -0.565685425 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + p = -0.565685425 + -0.6
p = -0.565685425 + -0.6

Combine like terms: -0.565685425 + -0.6 = -1.165685425
p = -1.165685425

Simplifying
p = -1.165685425

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.034314575, -1.165685425}