3(p^2-2p+1)=15

Solution for 3(p^2-2p+1)=15 equation:

Simplifying
3(p2 + -2p + 1) = 15

Reorder the terms:
3(1 + -2p + p2) = 15
(1 * 3 + -2p * 3 + p2 * 3) = 15
(3 + -6p + 3p2) = 15

Solving
3 + -6p + 3p2 = 15

Solving for variable 'p'.

Reorder the terms:
3 + -15 + -6p + 3p2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + -6p + 3p2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + -6p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -2p + p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -2p + p2)' equal to zero and attempt to solve:

Simplifying
-4 + -2p + p2 = 0

Solving
-4 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2p + 4 + p2 = 0 + 4

Reorder the terms:
-4 + 4 + -2p + p2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2p + p2 = 0 + 4
-2p + p2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2p + p2 = 4

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 4 + 1

Reorder the terms:
1 + -2p + p2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2p + p2 = 5

Factor a perfect square on the left side:
(p + -1)(p + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(p + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
p + -1 = 2.236067978

Simplifying
p + -1 = 2.236067978

Reorder the terms:
-1 + p = 2.236067978

Solving
-1 + p = 2.236067978

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + p = 2.236067978 + 1
p = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
p = 3.236067978

Simplifying
p = 3.236067978

Subproblem 2
p + -1 = -2.236067978

Simplifying
p + -1 = -2.236067978

Reorder the terms:
-1 + p = -2.236067978

Solving
-1 + p = -2.236067978

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + p = -2.236067978 + 1
p = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
p = -1.236067978

Simplifying
p = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.236067978, -1.236067978}
Solution
p = {3.236067978, -1.236067978}