4p^2+16p+3=5

Solution for 4p^2+16p+3=5 equation:

Simplifying
4p2 + 16p + 3 = 5

Reorder the terms:
3 + 16p + 4p2 = 5

Solving
3 + 16p + 4p2 = 5

Solving for variable 'p'.

Reorder the terms:
3 + -5 + 16p + 4p2 = 5 + -5

Combine like terms: 3 + -5 = -2
-2 + 16p + 4p2 = 5 + -5

Combine like terms: 5 + -5 = 0
-2 + 16p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 8p + 2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 8p + 2p2)' equal to zero and attempt to solve:

Simplifying
-1 + 8p + 2p2 = 0

Solving
-1 + 8p + 2p2 = 0

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

Divide each side by '2'.
-0.5 + 4p + p2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 4p + 0.5 + p2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 4p + p2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 4p + p2 = 0 + 0.5
4p + p2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
4p + p2 = 0.5

The p term is 4p.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4p + 4 + p2 = 0.5 + 4

Reorder the terms:
4 + 4p + p2 = 0.5 + 4

Combine like terms: 0.5 + 4 = 4.5
4 + 4p + p2 = 4.5

Factor a perfect square on the left side:
(p + 2)(p + 2) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(p + 2) equal to 2.121320344 and -2.121320344.

Subproblem 1
p + 2 = 2.121320344

Simplifying
p + 2 = 2.121320344

Reorder the terms:
2 + p = 2.121320344

Solving
2 + p = 2.121320344

Solving for variable 'p'.

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

Add '-2' to each side of the equation.
2 + -2 + p = 2.121320344 + -2

Combine like terms: 2 + -2 = 0
0 + p = 2.121320344 + -2
p = 2.121320344 + -2

Combine like terms: 2.121320344 + -2 = 0.121320344
p = 0.121320344

Simplifying
p = 0.121320344

Subproblem 2
p + 2 = -2.121320344

Simplifying
p + 2 = -2.121320344

Reorder the terms:
2 + p = -2.121320344

Solving
2 + p = -2.121320344

Solving for variable 'p'.

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

Add '-2' to each side of the equation.
2 + -2 + p = -2.121320344 + -2

Combine like terms: 2 + -2 = 0
0 + p = -2.121320344 + -2
p = -2.121320344 + -2

Combine like terms: -2.121320344 + -2 = -4.121320344
p = -4.121320344

Simplifying
p = -4.121320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.121320344, -4.121320344}
Solution
p = {0.121320344, -4.121320344}