2(p+3)3p=48

Solution for 2(p+3)3p=48 equation:

Simplifying
2(p + 3) * 3p = 48

Reorder the terms:
2(3 + p) * 3p = 48

Reorder the terms for easier multiplication:
2 * 3p(3 + p) = 48

Multiply 2 * 3
6p(3 + p) = 48
(3 * 6p + p * 6p) = 48
(18p + 6p2) = 48

Solving
18p + 6p2 = 48

Solving for variable 'p'.

Reorder the terms:
-48 + 18p + 6p2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 18p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + 3p + p2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-8 + 3p + p2)' equal to zero and attempt to solve:

Simplifying
-8 + 3p + p2 = 0

Solving
-8 + 3p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3p + 8 + p2 = 0 + 8

Reorder the terms:
-8 + 8 + 3p + p2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3p + p2 = 0 + 8
3p + p2 = 0 + 8

Combine like terms: 0 + 8 = 8
3p + p2 = 8

The p term is 3p.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3p + 2.25 + p2 = 8 + 2.25

Reorder the terms:
2.25 + 3p + p2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + 3p + p2 = 10.25

Factor a perfect square on the left side:
(p + 1.5)(p + 1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(p + 1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
p + 1.5 = 3.201562119

Simplifying
p + 1.5 = 3.201562119

Reorder the terms:
1.5 + p = 3.201562119

Solving
1.5 + p = 3.201562119

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = 3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = 3.201562119 + -1.5
p = 3.201562119 + -1.5

Combine like terms: 3.201562119 + -1.5 = 1.701562119
p = 1.701562119

Simplifying
p = 1.701562119

Subproblem 2
p + 1.5 = -3.201562119

Simplifying
p + 1.5 = -3.201562119

Reorder the terms:
1.5 + p = -3.201562119

Solving
1.5 + p = -3.201562119

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = -3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = -3.201562119 + -1.5
p = -3.201562119 + -1.5

Combine like terms: -3.201562119 + -1.5 = -4.701562119
p = -4.701562119

Simplifying
p = -4.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.701562119, -4.701562119}
Solution
p = {1.701562119, -4.701562119}