p^2=3p-2

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

Simplifying
p2 = 3p + -2

Reorder the terms:
p2 = -2 + 3p

Solving
p2 = -2 + 3p

Solving for variable 'p'.

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

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

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

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

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

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 '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

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

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

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {1, 2}