(2m-1)(m+3)=-2(m+4)

Solution for (2m-1)(m+3)=-2(m+4) equation:

Simplifying
(2m + -1)(m + 3) = -2(m + 4)

Reorder the terms:
(-1 + 2m)(m + 3) = -2(m + 4)

Reorder the terms:
(-1 + 2m)(3 + m) = -2(m + 4)

Multiply (-1 + 2m) * (3 + m)
(-1(3 + m) + 2m * (3 + m)) = -2(m + 4)
((3 * -1 + m * -1) + 2m * (3 + m)) = -2(m + 4)
((-3 + -1m) + 2m * (3 + m)) = -2(m + 4)
(-3 + -1m + (3 * 2m + m * 2m)) = -2(m + 4)
(-3 + -1m + (6m + 2m2)) = -2(m + 4)

Combine like terms: -1m + 6m = 5m
(-3 + 5m + 2m2) = -2(m + 4)

Reorder the terms:
-3 + 5m + 2m2 = -2(4 + m)
-3 + 5m + 2m2 = (4 * -2 + m * -2)
-3 + 5m + 2m2 = (-8 + -2m)

Solving
-3 + 5m + 2m2 = -8 + -2m

Solving for variable 'm'.

Reorder the terms:
-3 + 8 + 5m + 2m + 2m2 = -8 + -2m + 8 + 2m

Combine like terms: -3 + 8 = 5
5 + 5m + 2m + 2m2 = -8 + -2m + 8 + 2m

Combine like terms: 5m + 2m = 7m
5 + 7m + 2m2 = -8 + -2m + 8 + 2m

Reorder the terms:
5 + 7m + 2m2 = -8 + 8 + -2m + 2m

Combine like terms: -8 + 8 = 0
5 + 7m + 2m2 = 0 + -2m + 2m
5 + 7m + 2m2 = -2m + 2m

Combine like terms: -2m + 2m = 0
5 + 7m + 2m2 = 0

Factor a trinomial.
(5 + 2m)(1 + m) = 0

Subproblem 1
Set the factor '(5 + 2m)' equal to zero and attempt to solve:

Simplifying
5 + 2m = 0

Solving
5 + 2m = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2m = 0 + -5
2m = 0 + -5

Combine like terms: 0 + -5 = -5
2m = -5

Divide each side by '2'.
m = -2.5

Simplifying
m = -2.5
Subproblem 2
Set the factor '(1 + m)' equal to zero and attempt to solve:

Simplifying
1 + m = 0

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

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

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

Simplifying
m = -1
Solution
m = {-2.5, -1}