m^2*p^2-7mp+12=0

Solution for m^2*p^2-7mp+12=0 equation:

Simplifying
m2 * p2 + -7mp + 12 = 0

Multiply m2 * p2
m2p2 + -7mp + 12 = 0

Reorder the terms:
12 + -7mp + m2p2 = 0

Solving
12 + -7mp + m2p2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3 + -1mp)(4 + -1mp) = 0

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

Simplifying
3 + -1mp = 0

Solving
3 + -1mp = 0

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

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

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

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

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

Simplifying
m = 3p-1
Subproblem 2
Set the factor '(4 + -1mp)' equal to zero and attempt to solve:

Simplifying
4 + -1mp = 0

Solving
4 + -1mp = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1mp = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1mp = 0 + -4
-1mp = 0 + -4

Combine like terms: 0 + -4 = -4
-1mp = -4

Divide each side by '-1p'.
m = 4p-1

Simplifying
m = 4p-1
Solution
m = {3p-1, 4p-1}