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

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


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

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

Multiply (3 + 2m) * (3 + -1m)
4 = (3(3 + -1m) + 2m * (3 + -1m))
4 = ((3 * 3 + -1m * 3) + 2m * (3 + -1m))
4 = ((9 + -3m) + 2m * (3 + -1m))
4 = (9 + -3m + (3 * 2m + -1m * 2m))
4 = (9 + -3m + (6m + -2m2))

Combine like terms: -3m + 6m = 3m
4 = (9 + 3m + -2m2)

Solving
4 = 9 + 3m + -2m2

Solving for variable 'm'.

Combine like terms: 4 + -9 = -5
-5 + -3m + 2m2 = 9 + 3m + -2m2 + -9 + -3m + 2m2

Reorder the terms:
-5 + -3m + 2m2 = 9 + -9 + 3m + -3m + -2m2 + 2m2

Combine like terms: 9 + -9 = 0
-5 + -3m + 2m2 = 0 + 3m + -3m + -2m2 + 2m2
-5 + -3m + 2m2 = 3m + -3m + -2m2 + 2m2

Combine like terms: 3m + -3m = 0
-5 + -3m + 2m2 = 0 + -2m2 + 2m2
-5 + -3m + 2m2 = -2m2 + 2m2

Combine like terms: -2m2 + 2m2 = 0
-5 + -3m + 2m2 = 0

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


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 '(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
Solution
m = {-1, 2.5}

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