2=-2p^2+4p

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

Simplifying
2 = -2p2 + 4p

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

Solving
2 = 4p + -2p2

Solving for variable 'p'.

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

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

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

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

Factor a trinomial.
2((1 + -1p)(1 + -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 '(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
Solution
p = {1, 1}