3(2p-1)+2p(5p-10)=8p+9

Solution for 3(2p-1)+2p(5p-10)=8p+9 equation:

Simplifying
3(2p + -1) + 2p(5p + -10) = 8p + 9

Reorder the terms:
3(-1 + 2p) + 2p(5p + -10) = 8p + 9
(-1 * 3 + 2p * 3) + 2p(5p + -10) = 8p + 9
(-3 + 6p) + 2p(5p + -10) = 8p + 9

Reorder the terms:
-3 + 6p + 2p(-10 + 5p) = 8p + 9
-3 + 6p + (-10 * 2p + 5p * 2p) = 8p + 9
-3 + 6p + (-20p + 10p2) = 8p + 9

Combine like terms: 6p + -20p = -14p
-3 + -14p + 10p2 = 8p + 9

Reorder the terms:
-3 + -14p + 10p2 = 9 + 8p

Solving
-3 + -14p + 10p2 = 9 + 8p

Solving for variable 'p'.

Reorder the terms:
-3 + -9 + -14p + -8p + 10p2 = 9 + 8p + -9 + -8p

Combine like terms: -3 + -9 = -12
-12 + -14p + -8p + 10p2 = 9 + 8p + -9 + -8p

Combine like terms: -14p + -8p = -22p
-12 + -22p + 10p2 = 9 + 8p + -9 + -8p

Reorder the terms:
-12 + -22p + 10p2 = 9 + -9 + 8p + -8p

Combine like terms: 9 + -9 = 0
-12 + -22p + 10p2 = 0 + 8p + -8p
-12 + -22p + 10p2 = 8p + -8p

Combine like terms: 8p + -8p = 0
-12 + -22p + 10p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -11p + 5p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -11p + 5p2)' equal to zero and attempt to solve:

Simplifying
-6 + -11p + 5p2 = 0

Solving
-6 + -11p + 5p2 = 0

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

Divide each side by '5'.
-1.2 + -2.2p + p2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.2p + 1.2 + p2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.2p + p2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.2p + p2 = 0 + 1.2
-2.2p + p2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.2p + p2 = 1.2

The p term is -2.2p.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2p + 1.21 + p2 = 1.2 + 1.21

Reorder the terms:
1.21 + -2.2p + p2 = 1.2 + 1.21

Combine like terms: 1.2 + 1.21 = 2.41
1.21 + -2.2p + p2 = 2.41

Factor a perfect square on the left side:
(p + -1.1)(p + -1.1) = 2.41

Calculate the square root of the right side: 1.55241747

Break this problem into two subproblems by setting 
(p + -1.1) equal to 1.55241747 and -1.55241747.

Subproblem 1
p + -1.1 = 1.55241747

Simplifying
p + -1.1 = 1.55241747

Reorder the terms:
-1.1 + p = 1.55241747

Solving
-1.1 + p = 1.55241747

Solving for variable 'p'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + p = 1.55241747 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + p = 1.55241747 + 1.1
p = 1.55241747 + 1.1

Combine like terms: 1.55241747 + 1.1 = 2.65241747
p = 2.65241747

Simplifying
p = 2.65241747

Subproblem 2
p + -1.1 = -1.55241747

Simplifying
p + -1.1 = -1.55241747

Reorder the terms:
-1.1 + p = -1.55241747

Solving
-1.1 + p = -1.55241747

Solving for variable 'p'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + p = -1.55241747 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + p = -1.55241747 + 1.1
p = -1.55241747 + 1.1

Combine like terms: -1.55241747 + 1.1 = -0.45241747
p = -0.45241747

Simplifying
p = -0.45241747

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.65241747, -0.45241747}
Solution
p = {2.65241747, -0.45241747}