10p(p-3)-8=

Solution for 10p(p-3)-8= equation:

Simplifying
10p(p + -3) + -8 = 0

Reorder the terms:
10p(-3 + p) + -8 = 0
(-3 * 10p + p * 10p) + -8 = 0
(-30p + 10p2) + -8 = 0

Reorder the terms:
-8 + -30p + 10p2 = 0

Solving
-8 + -30p + 10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -15p + 5p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -15p + 5p2)' equal to zero and attempt to solve:

Simplifying
-4 + -15p + 5p2 = 0

Solving
-4 + -15p + 5p2 = 0

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

Divide each side by '5'.
-0.8 + -3p + p2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -3p + 0.8 + p2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -3p + p2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -3p + p2 = 0 + 0.8
-3p + p2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-3p + p2 = 0.8

The p term is -3p.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3p + 2.25 + p2 = 0.8 + 2.25

Reorder the terms:
2.25 + -3p + p2 = 0.8 + 2.25

Combine like terms: 0.8 + 2.25 = 3.05
2.25 + -3p + p2 = 3.05

Factor a perfect square on the left side:
(p + -1.5)(p + -1.5) = 3.05

Calculate the square root of the right side: 1.74642492

Break this problem into two subproblems by setting 
(p + -1.5) equal to 1.74642492 and -1.74642492.

Subproblem 1
p + -1.5 = 1.74642492

Simplifying
p + -1.5 = 1.74642492

Reorder the terms:
-1.5 + p = 1.74642492

Solving
-1.5 + p = 1.74642492

Solving for variable 'p'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + p = 1.74642492 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = 1.74642492 + 1.5
p = 1.74642492 + 1.5

Combine like terms: 1.74642492 + 1.5 = 3.24642492
p = 3.24642492

Simplifying
p = 3.24642492

Subproblem 2
p + -1.5 = -1.74642492

Simplifying
p + -1.5 = -1.74642492

Reorder the terms:
-1.5 + p = -1.74642492

Solving
-1.5 + p = -1.74642492

Solving for variable 'p'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + p = -1.74642492 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = -1.74642492 + 1.5
p = -1.74642492 + 1.5

Combine like terms: -1.74642492 + 1.5 = -0.24642492
p = -0.24642492

Simplifying
p = -0.24642492

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.24642492, -0.24642492}
Solution
p = {3.24642492, -0.24642492}