-3p(p-10)-6(5-3p)=

Solution for -3p(p-10)-6(5-3p)= equation:

Simplifying
-3p(p + -10) + -6(5 + -3p) = 0

Reorder the terms:
-3p(-10 + p) + -6(5 + -3p) = 0
(-10 * -3p + p * -3p) + -6(5 + -3p) = 0
(30p + -3p2) + -6(5 + -3p) = 0
30p + -3p2 + (5 * -6 + -3p * -6) = 0
30p + -3p2 + (-30 + 18p) = 0

Reorder the terms:
-30 + 30p + 18p + -3p2 = 0

Combine like terms: 30p + 18p = 48p
-30 + 48p + -3p2 = 0

Solving
-30 + 48p + -3p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 16p + -1p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + 16p + -1p2)' equal to zero and attempt to solve:

Simplifying
-10 + 16p + -1p2 = 0

Solving
-10 + 16p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -16p + p2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -16p + -10 + p2 = 0 + -10

Reorder the terms:
10 + -10 + -16p + p2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -16p + p2 = 0 + -10
-16p + p2 = 0 + -10

Combine like terms: 0 + -10 = -10
-16p + p2 = -10

The p term is -16p.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16p + 64 + p2 = -10 + 64

Reorder the terms:
64 + -16p + p2 = -10 + 64

Combine like terms: -10 + 64 = 54
64 + -16p + p2 = 54

Factor a perfect square on the left side:
(p + -8)(p + -8) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(p + -8) equal to 7.348469228 and -7.348469228.

Subproblem 1
p + -8 = 7.348469228

Simplifying
p + -8 = 7.348469228

Reorder the terms:
-8 + p = 7.348469228

Solving
-8 + p = 7.348469228

Solving for variable 'p'.

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

Add '8' to each side of the equation.
-8 + 8 + p = 7.348469228 + 8

Combine like terms: -8 + 8 = 0
0 + p = 7.348469228 + 8
p = 7.348469228 + 8

Combine like terms: 7.348469228 + 8 = 15.348469228
p = 15.348469228

Simplifying
p = 15.348469228

Subproblem 2
p + -8 = -7.348469228

Simplifying
p + -8 = -7.348469228

Reorder the terms:
-8 + p = -7.348469228

Solving
-8 + p = -7.348469228

Solving for variable 'p'.

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

Add '8' to each side of the equation.
-8 + 8 + p = -7.348469228 + 8

Combine like terms: -8 + 8 = 0
0 + p = -7.348469228 + 8
p = -7.348469228 + 8

Combine like terms: -7.348469228 + 8 = 0.651530772
p = 0.651530772

Simplifying
p = 0.651530772

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {15.348469228, 0.651530772}
Solution
p = {15.348469228, 0.651530772}