-3p(p+2)=-30

Solution for -3p(p+2)=-30 equation:

Simplifying
-3p(p + 2) = -30

Reorder the terms:
-3p(2 + p) = -30
(2 * -3p + p * -3p) = -30
(-6p + -3p2) = -30

Solving
-6p + -3p2 = -30

Solving for variable 'p'.

Reorder the terms:
30 + -6p + -3p2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -6p + -3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -2p + -1p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(10 + -2p + -1p2)' equal to zero and attempt to solve:

Simplifying
10 + -2p + -1p2 = 0

Solving
10 + -2p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + 2p + p2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2p + 10 + p2 = 0 + 10

Reorder the terms:
-10 + 10 + 2p + p2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2p + p2 = 0 + 10
2p + p2 = 0 + 10

Combine like terms: 0 + 10 = 10
2p + p2 = 10

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 = 10 + 1

Reorder the terms:
1 + 2p + p2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2p + p2 = 11

Factor a perfect square on the left side:
(p + 1)(p + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(p + 1) equal to 3.31662479 and -3.31662479.

Subproblem 1
p + 1 = 3.31662479

Simplifying
p + 1 = 3.31662479

Reorder the terms:
1 + p = 3.31662479

Solving
1 + p = 3.31662479

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 = 3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + p = 3.31662479 + -1
p = 3.31662479 + -1

Combine like terms: 3.31662479 + -1 = 2.31662479
p = 2.31662479

Simplifying
p = 2.31662479

Subproblem 2
p + 1 = -3.31662479

Simplifying
p + 1 = -3.31662479

Reorder the terms:
1 + p = -3.31662479

Solving
1 + p = -3.31662479

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 = -3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + p = -3.31662479 + -1
p = -3.31662479 + -1

Combine like terms: -3.31662479 + -1 = -4.31662479
p = -4.31662479

Simplifying
p = -4.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.31662479, -4.31662479}
Solution
p = {2.31662479, -4.31662479}