2p^2=6+4p

Solution for 2p^2=6+4p equation:

Simplifying
2p2 = 6 + 4p

Solving
2p2 = 6 + 4p

Solving for variable 'p'.

Reorder the terms:
-6 + -4p + 2p2 = 6 + 4p + -6 + -4p

Reorder the terms:
-6 + -4p + 2p2 = 6 + -6 + 4p + -4p

Combine like terms: 6 + -6 = 0
-6 + -4p + 2p2 = 0 + 4p + -4p
-6 + -4p + 2p2 = 4p + -4p

Combine like terms: 4p + -4p = 0
-6 + -4p + 2p2 = 0

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

Factor a trinomial.
2((-1 + -1p)(3 + -1p)) = 0

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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

Divide each side by '-1'.
p = -1

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

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

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

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

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

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-1, 3}