3(3p+3)3p=-3

Solution for 3(3p+3)3p=-3 equation:

Simplifying
3(3p + 3) * 3p = -3

Reorder the terms:
3(3 + 3p) * 3p = -3

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

Multiply 3 * 3
9p(3 + 3p) = -3
(3 * 9p + 3p * 9p) = -3
(27p + 27p2) = -3

Solving
27p + 27p2 = -3

Solving for variable 'p'.

Reorder the terms:
3 + 27p + 27p2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 27p + 27p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 9p + 9p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 9p + 9p2)' equal to zero and attempt to solve:

Simplifying
1 + 9p + 9p2 = 0

Solving
1 + 9p + 9p2 = 0

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

Divide each side by '9'.
0.1111111111 + p + p2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + p + -0.1111111111 + p2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + p + p2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + p + p2 = 0 + -0.1111111111
p + p2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
p + p2 = -0.1111111111

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + p2 = -0.1111111111 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + p2 = -0.1111111111 + 0.25

Combine like terms: -0.1111111111 + 0.25 = 0.1388888889
1.25 + p2 = 0.1388888889

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 0.1388888889

Calculate the square root of the right side: 0.372677996

Break this problem into two subproblems by setting 
(p + 0.5) equal to 0.372677996 and -0.372677996.

Subproblem 1
p + 0.5 = 0.372677996

Simplifying
p + 0.5 = 0.372677996

Reorder the terms:
0.5 + p = 0.372677996

Solving
0.5 + p = 0.372677996

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 0.372677996 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 0.372677996 + -0.5
p = 0.372677996 + -0.5

Combine like terms: 0.372677996 + -0.5 = -0.127322004
p = -0.127322004

Simplifying
p = -0.127322004

Subproblem 2
p + 0.5 = -0.372677996

Simplifying
p + 0.5 = -0.372677996

Reorder the terms:
0.5 + p = -0.372677996

Solving
0.5 + p = -0.372677996

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -0.372677996 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -0.372677996 + -0.5
p = -0.372677996 + -0.5

Combine like terms: -0.372677996 + -0.5 = -0.872677996
p = -0.872677996

Simplifying
p = -0.872677996

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.127322004, -0.872677996}
Solution
p = {-0.127322004, -0.872677996}