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

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

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

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

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

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

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

Solving
0 = 2 + 7m + 3m2

Solving for variable 'm'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 7m + 3m2) = 0

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

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

Simplifying
2 + m = 0

Solving
2 + m = 0

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

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

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

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

Simplifying
m = -2
Subproblem 2
Set the factor '(1 + 3m)' equal to zero and attempt to solve:

Simplifying
1 + 3m = 0

Solving
1 + 3m = 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 + 3m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3m = 0 + -1
3m = 0 + -1

Combine like terms: 0 + -1 = -1
3m = -1

Divide each side by '3'.
m = -0.3333333333

Simplifying
m = -0.3333333333
Solution
m = {-2, -0.3333333333}