6p^2+29p-20=0

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Solution for 6p^2+29p-20=0 equation: 


Simplifying
6p2 + 29p + -20 = 0

Reorder the terms:
-20 + 29p + 6p2 = 0

Solving
-20 + 29p + 6p2 = 0

Solving for variable 'p'.

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

Divide each side by '6'.
-3.333333333 + 4.833333333p + p2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 4.833333333p + 3.333333333 + p2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 4.833333333p + p2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 4.833333333p + p2 = 0 + 3.333333333
4.833333333p + p2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
4.833333333p + p2 = 3.333333333

The p term is 4.833333333p.  Take half its coefficient (2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
4.833333333p + 5.840277779 + p2 = 3.333333333 + 5.840277779

Reorder the terms:
5.840277779 + 4.833333333p + p2 = 3.333333333 + 5.840277779

Combine like terms: 3.333333333 + 5.840277779 = 9.173611112
5.840277779 + 4.833333333p + p2 = 9.173611112

Factor a perfect square on the left side:
(p + 2.416666667)(p + 2.416666667) = 9.173611112

Calculate the square root of the right side: 3.028796974

Break this problem into two subproblems by setting 
(p + 2.416666667) equal to 3.028796974 and -3.028796974.


Subproblem 1
p + 2.416666667 = 3.028796974

Simplifying
p + 2.416666667 = 3.028796974

Reorder the terms:
2.416666667 + p = 3.028796974

Solving
2.416666667 + p = 3.028796974

Solving for variable 'p'.

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

Add '-2.416666667' to each side of the equation.
2.416666667 + -2.416666667 + p = 3.028796974 + -2.416666667

Combine like terms: 2.416666667 + -2.416666667 = 0.000000000
0.000000000 + p = 3.028796974 + -2.416666667
p = 3.028796974 + -2.416666667

Combine like terms: 3.028796974 + -2.416666667 = 0.612130307
p = 0.612130307

Simplifying
p = 0.612130307


Subproblem 2
p + 2.416666667 = -3.028796974

Simplifying
p + 2.416666667 = -3.028796974

Reorder the terms:
2.416666667 + p = -3.028796974

Solving
2.416666667 + p = -3.028796974

Solving for variable 'p'.

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

Add '-2.416666667' to each side of the equation.
2.416666667 + -2.416666667 + p = -3.028796974 + -2.416666667

Combine like terms: 2.416666667 + -2.416666667 = 0.000000000
0.000000000 + p = -3.028796974 + -2.416666667
p = -3.028796974 + -2.416666667

Combine like terms: -3.028796974 + -2.416666667 = -5.445463641
p = -5.445463641

Simplifying
p = -5.445463641


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.612130307, -5.445463641}

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