(4m-1)(m+3)=0

Solution for (4m-1)(m+3)=0 equation:

Simplifying
(4m + -1)(m + 3) = 0

Reorder the terms:
(-1 + 4m)(m + 3) = 0

Reorder the terms:
(-1 + 4m)(3 + m) = 0

Multiply (-1 + 4m) * (3 + m)
(-1(3 + m) + 4m * (3 + m)) = 0
((3 * -1 + m * -1) + 4m * (3 + m)) = 0
((-3 + -1m) + 4m * (3 + m)) = 0
(-3 + -1m + (3 * 4m + m * 4m)) = 0
(-3 + -1m + (12m + 4m2)) = 0

Combine like terms: -1m + 12m = 11m
(-3 + 11m + 4m2) = 0

Solving
-3 + 11m + 4m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -1m)(1 + -4m) = 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 '(1 + -4m)' equal to zero and attempt to solve:

Simplifying
1 + -4m = 0

Solving
1 + -4m = 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 + -4m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4m = 0 + -1
-4m = 0 + -1

Combine like terms: 0 + -1 = -1
-4m = -1

Divide each side by '-4'.
m = 0.25

Simplifying
m = 0.25
Solution
m = {-3, 0.25}