4(3-m)-5m(m-3)=0

Solution for 4(3-m)-5m(m-3)=0 equation:

Simplifying
4(3 + -1m) + -5m(m + -3) = 0
(3 * 4 + -1m * 4) + -5m(m + -3) = 0
(12 + -4m) + -5m(m + -3) = 0

Reorder the terms:
12 + -4m + -5m(-3 + m) = 0
12 + -4m + (-3 * -5m + m * -5m) = 0
12 + -4m + (15m + -5m2) = 0

Combine like terms: -4m + 15m = 11m
12 + 11m + -5m2 = 0

Solving
12 + 11m + -5m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3 + -1m)(4 + 5m) = 0

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

Simplifying
3 + -1m = 0

Solving
3 + -1m = 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 + -1m = 0 + -3

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

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

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

Simplifying
m = 3
Subproblem 2
Set the factor '(4 + 5m)' equal to zero and attempt to solve:

Simplifying
4 + 5m = 0

Solving
4 + 5m = 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 + 5m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5m = 0 + -4
5m = 0 + -4

Combine like terms: 0 + -4 = -4
5m = -4

Divide each side by '5'.
m = -0.8

Simplifying
m = -0.8
Solution
m = {3, -0.8}