3p^2+10p-120=0

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Solution for 3p^2+10p-120=0 equation: 


Simplifying
3p2 + 10p + -120 = 0

Reorder the terms:
-120 + 10p + 3p2 = 0

Solving
-120 + 10p + 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'.
-40 + 3.333333333p + p2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 3.333333333p + 40 + p2 = 0 + 40

Reorder the terms:
-40 + 40 + 3.333333333p + p2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 3.333333333p + p2 = 0 + 40
3.333333333p + p2 = 0 + 40

Combine like terms: 0 + 40 = 40
3.333333333p + p2 = 40

The p term is 3.333333333p.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333p + 2.777777779 + p2 = 40 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333p + p2 = 40 + 2.777777779

Combine like terms: 40 + 2.777777779 = 42.777777779
2.777777779 + 3.333333333p + p2 = 42.777777779

Factor a perfect square on the left side:
(p + 1.666666667)(p + 1.666666667) = 42.777777779

Calculate the square root of the right side: 6.54047229

Break this problem into two subproblems by setting 
(p + 1.666666667) equal to 6.54047229 and -6.54047229.


Subproblem 1
p + 1.666666667 = 6.54047229

Simplifying
p + 1.666666667 = 6.54047229

Reorder the terms:
1.666666667 + p = 6.54047229

Solving
1.666666667 + p = 6.54047229

Solving for variable 'p'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + p = 6.54047229 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + p = 6.54047229 + -1.666666667
p = 6.54047229 + -1.666666667

Combine like terms: 6.54047229 + -1.666666667 = 4.873805623
p = 4.873805623

Simplifying
p = 4.873805623


Subproblem 2
p + 1.666666667 = -6.54047229

Simplifying
p + 1.666666667 = -6.54047229

Reorder the terms:
1.666666667 + p = -6.54047229

Solving
1.666666667 + p = -6.54047229

Solving for variable 'p'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + p = -6.54047229 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + p = -6.54047229 + -1.666666667
p = -6.54047229 + -1.666666667

Combine like terms: -6.54047229 + -1.666666667 = -8.207138957
p = -8.207138957

Simplifying
p = -8.207138957


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.873805623, -8.207138957}

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