p(2p-3)=12-3

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

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

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

Combine like terms: 12 + -3 = 9
-3p + 2p2 = 9

Solving
-3p + 2p2 = 9

Solving for variable 'p'.

Reorder the terms:
-9 + -3p + 2p2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -3p + 2p2 = 0

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

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

Simplifying
-3 + -2p = 0

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

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

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

Divide each side by '-2'.
p = -1.5

Simplifying
p = -1.5
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 = {-1.5, 3}