6p^2=24p+16+0

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Solution for 6p^2=24p+16+0 equation: 


Simplifying
6p2 = 24p + 16 + 0

Reorder the terms:
6p2 = 16 + 0 + 24p

Combine like terms: 16 + 0 = 16
6p2 = 16 + 24p

Solving
6p2 = 16 + 24p

Solving for variable 'p'.

Reorder the terms:
-16 + -24p + 6p2 = 16 + 24p + -16 + -24p

Reorder the terms:
-16 + -24p + 6p2 = 16 + -16 + 24p + -24p

Combine like terms: 16 + -16 = 0
-16 + -24p + 6p2 = 0 + 24p + -24p
-16 + -24p + 6p2 = 24p + -24p

Combine like terms: 24p + -24p = 0
-16 + -24p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -12p + 3p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -12p + 3p2)' equal to zero and attempt to solve:

Simplifying
-8 + -12p + 3p2 = 0

Solving
-8 + -12p + 3p2 = 0

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

Divide each side by '3'.
-2.666666667 + -4p + p2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -4p + 2.666666667 + p2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -4p + p2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -4p + p2 = 0 + 2.666666667
-4p + p2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-4p + p2 = 2.666666667

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 2.666666667 + 4

Reorder the terms:
4 + -4p + p2 = 2.666666667 + 4

Combine like terms: 2.666666667 + 4 = 6.666666667
4 + -4p + p2 = 6.666666667

Factor a perfect square on the left side:
(p + -2)(p + -2) = 6.666666667

Calculate the square root of the right side: 2.581988898

Break this problem into two subproblems by setting 
(p + -2) equal to 2.581988898 and -2.581988898.


Subproblem 1
p + -2 = 2.581988898

Simplifying
p + -2 = 2.581988898

Reorder the terms:
-2 + p = 2.581988898

Solving
-2 + p = 2.581988898

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = 2.581988898 + 2

Combine like terms: -2 + 2 = 0
0 + p = 2.581988898 + 2
p = 2.581988898 + 2

Combine like terms: 2.581988898 + 2 = 4.581988898
p = 4.581988898

Simplifying
p = 4.581988898


Subproblem 2
p + -2 = -2.581988898

Simplifying
p + -2 = -2.581988898

Reorder the terms:
-2 + p = -2.581988898

Solving
-2 + p = -2.581988898

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = -2.581988898 + 2

Combine like terms: -2 + 2 = 0
0 + p = -2.581988898 + 2
p = -2.581988898 + 2

Combine like terms: -2.581988898 + 2 = -0.581988898
p = -0.581988898

Simplifying
p = -0.581988898


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.581988898, -0.581988898}
Solution
p = {4.581988898, -0.581988898}

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