3p(p-1)=2(1-p)

Solution for 3p(p-1)=2(1-p) equation:

Simplifying
3p(p + -1) = 2(1 + -1p)

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

Solving
-3p + 3p2 = 2 + -2p

Solving for variable 'p'.

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

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

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

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

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

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

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

Simplifying
-2 + -3p = 0

Solving
-2 + -3p = 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 + -3p = 0 + 2

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

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

Divide each side by '-3'.
p = -0.6666666667

Simplifying
p = -0.6666666667
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 = {-0.6666666667, 1}