2p^2+2=6p

Solution for 2p^2+2=6p equation:

Simplifying
2p2 + 2 = 6p

Reorder the terms:
2 + 2p2 = 6p

Solving
2 + 2p2 = 6p

Solving for variable 'p'.

Reorder the terms:
2 + -6p + 2p2 = 6p + -6p

Combine like terms: 6p + -6p = 0
2 + -6p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -3p + p2) = 0

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

Simplifying
1 + -3p + p2 = 0

Solving
1 + -3p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3p + -1 + p2 = 0 + -1

Reorder the terms:
1 + -1 + -3p + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3p + p2 = 0 + -1
-3p + p2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3p + p2 = -1

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 = -1 + 2.25

Reorder the terms:
2.25 + -3p + p2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3p + p2 = 1.25

Factor a perfect square on the left side:
(p + -1.5)(p + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(p + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
p + -1.5 = 1.118033989

Simplifying
p + -1.5 = 1.118033989

Reorder the terms:
-1.5 + p = 1.118033989

Solving
-1.5 + p = 1.118033989

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 = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = 1.118033989 + 1.5
p = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
p = 2.618033989

Simplifying
p = 2.618033989

Subproblem 2
p + -1.5 = -1.118033989

Simplifying
p + -1.5 = -1.118033989

Reorder the terms:
-1.5 + p = -1.118033989

Solving
-1.5 + p = -1.118033989

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 = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = -1.118033989 + 1.5
p = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
p = 0.381966011

Simplifying
p = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.618033989, 0.381966011}
Solution
p = {2.618033989, 0.381966011}