(m+5)(3m+4)=3(m+2)-2

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Solution for (m+5)(3m+4)=3(m+2)-2 equation: 


Simplifying
(m + 5)(3m + 4) = 3(m + 2) + -2

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

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

Multiply (5 + m) * (4 + 3m)
(5(4 + 3m) + m(4 + 3m)) = 3(m + 2) + -2
((4 * 5 + 3m * 5) + m(4 + 3m)) = 3(m + 2) + -2
((20 + 15m) + m(4 + 3m)) = 3(m + 2) + -2
(20 + 15m + (4 * m + 3m * m)) = 3(m + 2) + -2
(20 + 15m + (4m + 3m2)) = 3(m + 2) + -2

Combine like terms: 15m + 4m = 19m
(20 + 19m + 3m2) = 3(m + 2) + -2

Reorder the terms:
20 + 19m + 3m2 = 3(2 + m) + -2
20 + 19m + 3m2 = (2 * 3 + m * 3) + -2
20 + 19m + 3m2 = (6 + 3m) + -2

Reorder the terms:
20 + 19m + 3m2 = 6 + -2 + 3m

Combine like terms: 6 + -2 = 4
20 + 19m + 3m2 = 4 + 3m

Solving
20 + 19m + 3m2 = 4 + 3m

Solving for variable 'm'.

Reorder the terms:
20 + -4 + 19m + -3m + 3m2 = 4 + 3m + -4 + -3m

Combine like terms: 20 + -4 = 16
16 + 19m + -3m + 3m2 = 4 + 3m + -4 + -3m

Combine like terms: 19m + -3m = 16m
16 + 16m + 3m2 = 4 + 3m + -4 + -3m

Reorder the terms:
16 + 16m + 3m2 = 4 + -4 + 3m + -3m

Combine like terms: 4 + -4 = 0
16 + 16m + 3m2 = 0 + 3m + -3m
16 + 16m + 3m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
16 + 16m + 3m2 = 0

Factor a trinomial.
(4 + m)(4 + 3m) = 0


Subproblem 1
Set the factor '(4 + m)' equal to zero and attempt to solve:

Simplifying
4 + m = 0

Solving
4 + m = 0

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

Add '-4' to each side of the equation.
4 + -4 + m = 0 + -4

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

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

Simplifying
m = -4

Subproblem 2
Set the factor '(4 + 3m)' equal to zero and attempt to solve:

Simplifying
4 + 3m = 0

Solving
4 + 3m = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3m = 0 + -4

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

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

Divide each side by '3'.
m = -1.333333333

Simplifying
m = -1.333333333
Solution
m = {-4, -1.333333333}

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