2p*3(p+3)=21

Solution for 2p*3(p+3)=21 equation:

Simplifying
2p * 3(p + 3) = 21

Reorder the terms:
2p * 3(3 + p) = 21

Reorder the terms for easier multiplication:
2 * 3p(3 + p) = 21

Multiply 2 * 3
6p(3 + p) = 21
(3 * 6p + p * 6p) = 21
(18p + 6p2) = 21

Solving
18p + 6p2 = 21

Solving for variable 'p'.

Reorder the terms:
-21 + 18p + 6p2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 18p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 6p + 2p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + 6p + 2p2)' equal to zero and attempt to solve:

Simplifying
-7 + 6p + 2p2 = 0

Solving
-7 + 6p + 2p2 = 0

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

Divide each side by '2'.
-3.5 + 3p + p2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 3p + 3.5 + p2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 3p + p2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 3p + p2 = 0 + 3.5
3p + p2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
3p + p2 = 3.5

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 = 3.5 + 2.25

Reorder the terms:
2.25 + 3p + p2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + 3p + p2 = 5.75

Factor a perfect square on the left side:
(p + 1.5)(p + 1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(p + 1.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
p + 1.5 = 2.397915762

Simplifying
p + 1.5 = 2.397915762

Reorder the terms:
1.5 + p = 2.397915762

Solving
1.5 + p = 2.397915762

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 = 2.397915762 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = 2.397915762 + -1.5
p = 2.397915762 + -1.5

Combine like terms: 2.397915762 + -1.5 = 0.897915762
p = 0.897915762

Simplifying
p = 0.897915762

Subproblem 2
p + 1.5 = -2.397915762

Simplifying
p + 1.5 = -2.397915762

Reorder the terms:
1.5 + p = -2.397915762

Solving
1.5 + p = -2.397915762

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 = -2.397915762 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = -2.397915762 + -1.5
p = -2.397915762 + -1.5

Combine like terms: -2.397915762 + -1.5 = -3.897915762
p = -3.897915762

Simplifying
p = -3.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.897915762, -3.897915762}
Solution
p = {0.897915762, -3.897915762}