3p^2-12p+4=0

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Solution for 3p^2-12p+4=0 equation: 


Simplifying
3p2 + -12p + 4 = 0

Reorder the terms:
4 + -12p + 3p2 = 0

Solving
4 + -12p + 3p2 = 0

Solving for variable 'p'.

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

Divide each side by '3'.
1.333333333 + -4p + p2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -4p + -1.333333333 + p2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -4p + p2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -4p + p2 = 0 + -1.333333333
-4p + p2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-4p + p2 = -1.333333333

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 = -1.333333333 + 4

Reorder the terms:
4 + -4p + p2 = -1.333333333 + 4

Combine like terms: -1.333333333 + 4 = 2.666666667
4 + -4p + p2 = 2.666666667

Factor a perfect square on the left side:
(p + -2)(p + -2) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(p + -2) equal to 1.632993162 and -1.632993162.


Subproblem 1
p + -2 = 1.632993162

Simplifying
p + -2 = 1.632993162

Reorder the terms:
-2 + p = 1.632993162

Solving
-2 + p = 1.632993162

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 = 1.632993162 + 2

Combine like terms: -2 + 2 = 0
0 + p = 1.632993162 + 2
p = 1.632993162 + 2

Combine like terms: 1.632993162 + 2 = 3.632993162
p = 3.632993162

Simplifying
p = 3.632993162


Subproblem 2
p + -2 = -1.632993162

Simplifying
p + -2 = -1.632993162

Reorder the terms:
-2 + p = -1.632993162

Solving
-2 + p = -1.632993162

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 = -1.632993162 + 2

Combine like terms: -2 + 2 = 0
0 + p = -1.632993162 + 2
p = -1.632993162 + 2

Combine like terms: -1.632993162 + 2 = 0.367006838
p = 0.367006838

Simplifying
p = 0.367006838


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.632993162, 0.367006838}

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