(6m-3)(m+1)=0

Solution for (6m-3)(m+1)=0 equation:

Simplifying
(6m + -3)(m + 1) = 0

Reorder the terms:
(-3 + 6m)(m + 1) = 0

Reorder the terms:
(-3 + 6m)(1 + m) = 0

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

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

Solving
-3 + 3m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + m + 2m2) = 0

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

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

Simplifying
-1 + -1m = 0

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

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

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

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

Simplifying
m = -1
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 = {-1, 0.5}