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

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

Simplifying
(3p + -1m)(p + 2m) = 0

Reorder the terms:
(-1m + 3p)(p + 2m) = 0

Reorder the terms:
(-1m + 3p)(2m + p) = 0

Multiply (-1m + 3p) * (2m + p)
(-1m * (2m + p) + 3p * (2m + p)) = 0
((2m * -1m + p * -1m) + 3p * (2m + p)) = 0

Reorder the terms:
((-1mp + -2m2) + 3p * (2m + p)) = 0
((-1mp + -2m2) + 3p * (2m + p)) = 0
(-1mp + -2m2 + (2m * 3p + p * 3p)) = 0
(-1mp + -2m2 + (6mp + 3p2)) = 0

Reorder the terms:
(-1mp + 6mp + -2m2 + 3p2) = 0

Combine like terms: -1mp + 6mp = 5mp
(5mp + -2m2 + 3p2) = 0

Solving
5mp + -2m2 + 3p2 = 0

Solving for variable 'm'.

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

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

Simplifying
-2m + -1p = 0

Solving
-2m + -1p = 0

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

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

Combine like terms: -1p + p = 0
-2m + 0 = 0 + p
-2m = 0 + p
Remove the zero:
-2m = p

Divide each side by '-2'.
m = -0.5p

Simplifying
m = -0.5p
Subproblem 2
Set the factor '(m + -3p)' equal to zero and attempt to solve:

Simplifying
m + -3p = 0

Solving
m + -3p = 0

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

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

Combine like terms: -3p + 3p = 0
m + 0 = 0 + 3p
m = 0 + 3p
Remove the zero:
m = 3p

Simplifying
m = 3p
Solution
m = {-0.5p, 3p}