(2mn-3)(5mn+2)=

Solution for (2mn-3)(5mn+2)= equation:

Simplifying
(2mn + -3)(5mn + 2) = 0

Reorder the terms:
(-3 + 2mn)(5mn + 2) = 0

Reorder the terms:
(-3 + 2mn)(2 + 5mn) = 0

Multiply (-3 + 2mn) * (2 + 5mn)
(-3(2 + 5mn) + 2mn * (2 + 5mn)) = 0
((2 * -3 + 5mn * -3) + 2mn * (2 + 5mn)) = 0
((-6 + -15mn) + 2mn * (2 + 5mn)) = 0
(-6 + -15mn + (2 * 2mn + 5mn * 2mn)) = 0
(-6 + -15mn + (4mn + 10m2n2)) = 0

Combine like terms: -15mn + 4mn = -11mn
(-6 + -11mn + 10m2n2) = 0

Solving
-6 + -11mn + 10m2n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-2 + -5mn)(3 + -2mn) = 0

Subproblem 1
Set the factor '(-2 + -5mn)' equal to zero and attempt to solve:

Simplifying
-2 + -5mn = 0

Solving
-2 + -5mn = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5mn = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5mn = 0 + 2
-5mn = 0 + 2

Combine like terms: 0 + 2 = 2
-5mn = 2

Divide each side by '-5n'.
m = -0.4n-1

Simplifying
m = -0.4n-1
Subproblem 2
Set the factor '(3 + -2mn)' equal to zero and attempt to solve:

Simplifying
3 + -2mn = 0

Solving
3 + -2mn = 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 + -2mn = 0 + -3

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

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

Divide each side by '-2n'.
m = 1.5n-1

Simplifying
m = 1.5n-1
Solution
m = {-0.4n-1, 1.5n-1}