2p^2+1=3p

Solution for 2p^2+1=3p equation:

Simplifying
2p2 + 1 = 3p

Reorder the terms:
1 + 2p2 = 3p

Solving
1 + 2p2 = 3p

Solving for variable 'p'.

Reorder the terms:
1 + -3p + 2p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
1 + -3p + 2p2 = 0

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

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

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
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 = {0.5, 1}