6(1+p)+6p(3p+5)=

Solution for 6(1+p)+6p(3p+5)= equation:

Simplifying
6(1 + p) + 6p(3p + 5) = 0
(1 * 6 + p * 6) + 6p(3p + 5) = 0
(6 + 6p) + 6p(3p + 5) = 0

Reorder the terms:
6 + 6p + 6p(5 + 3p) = 0
6 + 6p + (5 * 6p + 3p * 6p) = 0
6 + 6p + (30p + 18p2) = 0

Combine like terms: 6p + 30p = 36p
6 + 36p + 18p2 = 0

Solving
6 + 36p + 18p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 6p + 3p2) = 0

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

Simplifying
1 + 6p + 3p2 = 0

Solving
1 + 6p + 3p2 = 0

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

Divide each side by '3'.
0.3333333333 + 2p + p2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 2p + -0.3333333333 + p2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 2p + p2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 2p + p2 = 0 + -0.3333333333
2p + p2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
2p + p2 = -0.3333333333

The p term is 2p.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2p + 1 + p2 = -0.3333333333 + 1

Reorder the terms:
1 + 2p + p2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + 2p + p2 = 0.6666666667

Factor a perfect square on the left side:
(p + 1)(p + 1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(p + 1) equal to 0.816496581 and -0.816496581.

Subproblem 1
p + 1 = 0.816496581

Simplifying
p + 1 = 0.816496581

Reorder the terms:
1 + p = 0.816496581

Solving
1 + p = 0.816496581

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = 0.816496581 + -1

Combine like terms: 1 + -1 = 0
0 + p = 0.816496581 + -1
p = 0.816496581 + -1

Combine like terms: 0.816496581 + -1 = -0.183503419
p = -0.183503419

Simplifying
p = -0.183503419

Subproblem 2
p + 1 = -0.816496581

Simplifying
p + 1 = -0.816496581

Reorder the terms:
1 + p = -0.816496581

Solving
1 + p = -0.816496581

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = -0.816496581 + -1

Combine like terms: 1 + -1 = 0
0 + p = -0.816496581 + -1
p = -0.816496581 + -1

Combine like terms: -0.816496581 + -1 = -1.816496581
p = -1.816496581

Simplifying
p = -1.816496581

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.183503419, -1.816496581}
Solution
p = {-0.183503419, -1.816496581}