p(2p-3)=12-p

Solution for p(2p-3)=12-p equation:

Simplifying
p(2p + -3) = 12 + -1p

Reorder the terms:
p(-3 + 2p) = 12 + -1p
(-3 * p + 2p * p) = 12 + -1p
(-3p + 2p2) = 12 + -1p

Solving
-3p + 2p2 = 12 + -1p

Solving for variable 'p'.

Reorder the terms:
-12 + -3p + p + 2p2 = 12 + -1p + -12 + p

Combine like terms: -3p + p = -2p
-12 + -2p + 2p2 = 12 + -1p + -12 + p

Reorder the terms:
-12 + -2p + 2p2 = 12 + -12 + -1p + p

Combine like terms: 12 + -12 = 0
-12 + -2p + 2p2 = 0 + -1p + p
-12 + -2p + 2p2 = -1p + p

Combine like terms: -1p + p = 0
-12 + -2p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1p + p2) = 0

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

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

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

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

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

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-2, 3}