3p^2+14p+12=0

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Solution for 3p^2+14p+12=0 equation: 


Simplifying
3p2 + 14p + 12 = 0

Reorder the terms:
12 + 14p + 3p2 = 0

Solving
12 + 14p + 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'.
4 + 4.666666667p + p2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 4.666666667p + -4 + p2 = 0 + -4

Reorder the terms:
4 + -4 + 4.666666667p + p2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 4.666666667p + p2 = 0 + -4
4.666666667p + p2 = 0 + -4

Combine like terms: 0 + -4 = -4
4.666666667p + p2 = -4

The p term is 4.666666667p.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667p + 5.444444448 + p2 = -4 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667p + p2 = -4 + 5.444444448

Combine like terms: -4 + 5.444444448 = 1.444444448
5.444444448 + 4.666666667p + p2 = 1.444444448

Factor a perfect square on the left side:
(p + 2.333333334)(p + 2.333333334) = 1.444444448

Calculate the square root of the right side: 1.201850427

Break this problem into two subproblems by setting 
(p + 2.333333334) equal to 1.201850427 and -1.201850427.


Subproblem 1
p + 2.333333334 = 1.201850427

Simplifying
p + 2.333333334 = 1.201850427

Reorder the terms:
2.333333334 + p = 1.201850427

Solving
2.333333334 + p = 1.201850427

Solving for variable 'p'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + p = 1.201850427 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + p = 1.201850427 + -2.333333334
p = 1.201850427 + -2.333333334

Combine like terms: 1.201850427 + -2.333333334 = -1.131482907
p = -1.131482907

Simplifying
p = -1.131482907


Subproblem 2
p + 2.333333334 = -1.201850427

Simplifying
p + 2.333333334 = -1.201850427

Reorder the terms:
2.333333334 + p = -1.201850427

Solving
2.333333334 + p = -1.201850427

Solving for variable 'p'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + p = -1.201850427 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + p = -1.201850427 + -2.333333334
p = -1.201850427 + -2.333333334

Combine like terms: -1.201850427 + -2.333333334 = -3.535183761
p = -3.535183761

Simplifying
p = -3.535183761


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-1.131482907, -3.535183761}

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