(3m+7)(2m-1)=0

Solution for (3m+7)(2m-1)=0 equation:

Simplifying
(3m + 7)(2m + -1) = 0

Reorder the terms:
(7 + 3m)(2m + -1) = 0

Reorder the terms:
(7 + 3m)(-1 + 2m) = 0

Multiply (7 + 3m) * (-1 + 2m)
(7(-1 + 2m) + 3m * (-1 + 2m)) = 0
((-1 * 7 + 2m * 7) + 3m * (-1 + 2m)) = 0
((-7 + 14m) + 3m * (-1 + 2m)) = 0
(-7 + 14m + (-1 * 3m + 2m * 3m)) = 0
(-7 + 14m + (-3m + 6m2)) = 0

Combine like terms: 14m + -3m = 11m
(-7 + 11m + 6m2) = 0

Solving
-7 + 11m + 6m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-7 + -3m)(1 + -2m) = 0

Subproblem 1
Set the factor '(-7 + -3m)' equal to zero and attempt to solve:

Simplifying
-7 + -3m = 0

Solving
-7 + -3m = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3m = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3m = 0 + 7
-3m = 0 + 7

Combine like terms: 0 + 7 = 7
-3m = 7

Divide each side by '-3'.
m = -2.333333333

Simplifying
m = -2.333333333
Subproblem 2
Set the factor '(1 + -2m)' equal to zero and attempt to solve:

Simplifying
1 + -2m = 0

Solving
1 + -2m = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2m = 0 + -1

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

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

Divide each side by '-2'.
m = 0.5

Simplifying
m = 0.5
Solution
m = {-2.333333333, 0.5}