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

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

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

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

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

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

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

Solving
-1mp + m2 + -6p2 = 0

Solving for variable 'm'.

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

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

Simplifying
m + 2p = 0

Solving
m + 2p = 0

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

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

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

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