3p^2-6p=60

Solution for 3p^2-6p=60 equation:

Simplifying
3p2 + -6p = 60

Reorder the terms:
-6p + 3p2 = 60

Solving
-6p + 3p2 = 60

Solving for variable 'p'.

Reorder the terms:
-60 + -6p + 3p2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -6p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -2p + p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-20 + -2p + p2)' equal to zero and attempt to solve:

Simplifying
-20 + -2p + p2 = 0

Solving
-20 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2p + 20 + p2 = 0 + 20

Reorder the terms:
-20 + 20 + -2p + p2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2p + p2 = 0 + 20
-2p + p2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2p + p2 = 20

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 = 20 + 1

Reorder the terms:
1 + -2p + p2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2p + p2 = 21

Factor a perfect square on the left side:
(p + -1)(p + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(p + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1
p + -1 = 4.582575695

Simplifying
p + -1 = 4.582575695

Reorder the terms:
-1 + p = 4.582575695

Solving
-1 + p = 4.582575695

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 = 4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + p = 4.582575695 + 1
p = 4.582575695 + 1

Combine like terms: 4.582575695 + 1 = 5.582575695
p = 5.582575695

Simplifying
p = 5.582575695

Subproblem 2
p + -1 = -4.582575695

Simplifying
p + -1 = -4.582575695

Reorder the terms:
-1 + p = -4.582575695

Solving
-1 + p = -4.582575695

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 = -4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + p = -4.582575695 + 1
p = -4.582575695 + 1

Combine like terms: -4.582575695 + 1 = -3.582575695
p = -3.582575695

Simplifying
p = -3.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.582575695, -3.582575695}
Solution
p = {5.582575695, -3.582575695}