3p(p-2)=p-2

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

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

Reorder the terms:
3p(-2 + p) = p + -2
(-2 * 3p + p * 3p) = p + -2
(-6p + 3p2) = p + -2

Reorder the terms:
-6p + 3p2 = -2 + p

Solving
-6p + 3p2 = -2 + p

Solving for variable 'p'.

Reorder the terms:
2 + -6p + -1p + 3p2 = -2 + p + 2 + -1p

Combine like terms: -6p + -1p = -7p
2 + -7p + 3p2 = -2 + p + 2 + -1p

Reorder the terms:
2 + -7p + 3p2 = -2 + 2 + p + -1p

Combine like terms: -2 + 2 = 0
2 + -7p + 3p2 = 0 + p + -1p
2 + -7p + 3p2 = p + -1p

Combine like terms: p + -1p = 0
2 + -7p + 3p2 = 0

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

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

Simplifying
1 + -3p = 0

Solving
1 + -3p = 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 + -3p = 0 + -1

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

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

Divide each side by '-3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
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 = {0.3333333333, 2}