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

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


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

Reorder the terms:
0 = (m(3 + m)) + -1((m + 2)(3m + 1))
0 = ((3 * m + m * m)) + -1((m + 2)(3m + 1))
0 = ((3m + m2)) + -1((m + 2)(3m + 1))
0 = (3m + m2) + -1((m + 2)(3m + 1))

Remove parenthesis around (3m + m2)
0 = 3m + m2 + -1((m + 2)(3m + 1))

Reorder the terms:
0 = 3m + m2 + -1((2 + m)(3m + 1))

Reorder the terms:
0 = 3m + m2 + -1((2 + m)(1 + 3m))

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

Combine like terms: 6m + 1m = 7m
0 = 3m + m2 + -1((2 + 7m + 3m2))
0 = 3m + m2 + (2 * -1 + 7m * -1 + 3m2 * -1)
0 = 3m + m2 + (-2 + -7m + -3m2)

Reorder the terms:
0 = -2 + 3m + -7m + m2 + -3m2

Combine like terms: 3m + -7m = -4m
0 = -2 + -4m + m2 + -3m2

Combine like terms: m2 + -3m2 = -2m2
0 = -2 + -4m + -2m2

Solving
0 = -2 + -4m + -2m2

Solving for variable 'm'.

Combine like terms: 0 + 2 = 2
2 + 4m + 2m2 = -2 + -4m + -2m2 + 2 + 4m + 2m2

Reorder the terms:
2 + 4m + 2m2 = -2 + 2 + -4m + 4m + -2m2 + 2m2

Combine like terms: -2 + 2 = 0
2 + 4m + 2m2 = 0 + -4m + 4m + -2m2 + 2m2
2 + 4m + 2m2 = -4m + 4m + -2m2 + 2m2

Combine like terms: -4m + 4m = 0
2 + 4m + 2m2 = 0 + -2m2 + 2m2
2 + 4m + 2m2 = -2m2 + 2m2

Combine like terms: -2m2 + 2m2 = 0
2 + 4m + 2m2 = 0

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

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

Ignore the factor 2.

Subproblem 1
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

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 = {-1, -1}

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