-3p^2-75p-57=0

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Solution for -3p^2-75p-57=0 equation: 


Simplifying
-3p2 + -75p + -57 = 0

Reorder the terms:
-57 + -75p + -3p2 = 0

Solving
-57 + -75p + -3p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(19 + 25p + p2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(19 + 25p + p2)' equal to zero and attempt to solve:

Simplifying
19 + 25p + p2 = 0

Solving
19 + 25p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 25p + -19 + p2 = 0 + -19

Reorder the terms:
19 + -19 + 25p + p2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 25p + p2 = 0 + -19
25p + p2 = 0 + -19

Combine like terms: 0 + -19 = -19
25p + p2 = -19

The p term is 25p.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25p + 156.25 + p2 = -19 + 156.25

Reorder the terms:
156.25 + 25p + p2 = -19 + 156.25

Combine like terms: -19 + 156.25 = 137.25
156.25 + 25p + p2 = 137.25

Factor a perfect square on the left side:
(p + 12.5)(p + 12.5) = 137.25

Calculate the square root of the right side: 11.715374514

Break this problem into two subproblems by setting 
(p + 12.5) equal to 11.715374514 and -11.715374514.


Subproblem 1
p + 12.5 = 11.715374514

Simplifying
p + 12.5 = 11.715374514

Reorder the terms:
12.5 + p = 11.715374514

Solving
12.5 + p = 11.715374514

Solving for variable 'p'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + p = 11.715374514 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + p = 11.715374514 + -12.5
p = 11.715374514 + -12.5

Combine like terms: 11.715374514 + -12.5 = -0.784625486
p = -0.784625486

Simplifying
p = -0.784625486


Subproblem 2
p + 12.5 = -11.715374514

Simplifying
p + 12.5 = -11.715374514

Reorder the terms:
12.5 + p = -11.715374514

Solving
12.5 + p = -11.715374514

Solving for variable 'p'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + p = -11.715374514 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + p = -11.715374514 + -12.5
p = -11.715374514 + -12.5

Combine like terms: -11.715374514 + -12.5 = -24.215374514
p = -24.215374514

Simplifying
p = -24.215374514


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.784625486, -24.215374514}
Solution
p = {-0.784625486, -24.215374514}

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