3p^2+24p-6=0

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Solution for 3p^2+24p-6=0 equation: 


Simplifying
3p2 + 24p + -6 = 0

Reorder the terms:
-6 + 24p + 3p2 = 0

Solving
-6 + 24p + 3p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 8p + p2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + 8p + p2)' equal to zero and attempt to solve:

Simplifying
-2 + 8p + p2 = 0

Solving
-2 + 8p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + 8p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8p + p2 = 0 + 2
8p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
8p + p2 = 2

The p term is 8p.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8p + 16 + p2 = 2 + 16

Reorder the terms:
16 + 8p + p2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + 8p + p2 = 18

Factor a perfect square on the left side:
(p + 4)(p + 4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(p + 4) equal to 4.242640687 and -4.242640687.


Subproblem 1
p + 4 = 4.242640687

Simplifying
p + 4 = 4.242640687

Reorder the terms:
4 + p = 4.242640687

Solving
4 + p = 4.242640687

Solving for variable 'p'.

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

Add '-4' to each side of the equation.
4 + -4 + p = 4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + p = 4.242640687 + -4
p = 4.242640687 + -4

Combine like terms: 4.242640687 + -4 = 0.242640687
p = 0.242640687

Simplifying
p = 0.242640687


Subproblem 2
p + 4 = -4.242640687

Simplifying
p + 4 = -4.242640687

Reorder the terms:
4 + p = -4.242640687

Solving
4 + p = -4.242640687

Solving for variable 'p'.

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

Add '-4' to each side of the equation.
4 + -4 + p = -4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + p = -4.242640687 + -4
p = -4.242640687 + -4

Combine like terms: -4.242640687 + -4 = -8.242640687
p = -8.242640687

Simplifying
p = -8.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.242640687, -8.242640687}
Solution
p = {0.242640687, -8.242640687}

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