(4m+8)(2m-3)=0

Solution for (4m+8)(2m-3)=0 equation:

Simplifying
(4m + 8)(2m + -3) = 0

Reorder the terms:
(8 + 4m)(2m + -3) = 0

Reorder the terms:
(8 + 4m)(-3 + 2m) = 0

Multiply (8 + 4m) * (-3 + 2m)
(8(-3 + 2m) + 4m * (-3 + 2m)) = 0
((-3 * 8 + 2m * 8) + 4m * (-3 + 2m)) = 0
((-24 + 16m) + 4m * (-3 + 2m)) = 0
(-24 + 16m + (-3 * 4m + 2m * 4m)) = 0
(-24 + 16m + (-12m + 8m2)) = 0

Combine like terms: 16m + -12m = 4m
(-24 + 4m + 8m2) = 0

Solving
-24 + 4m + 8m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + m + 2m2) = 0

Factor a trinomial.
4((-2 + -1m)(3 + -2m)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -1m)' equal to zero and attempt to solve:

Simplifying
-2 + -1m = 0

Solving
-2 + -1m = 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 + -1m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1m = 0 + 2
-1m = 0 + 2

Combine like terms: 0 + 2 = 2
-1m = 2

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

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

Simplifying
3 + -2m = 0

Solving
3 + -2m = 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 + -2m = 0 + -3

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

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

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

Simplifying
m = 1.5
Solution
m = {-2, 1.5}