(m-3)(3m+4)=5(m+1)+8

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Solution for (m-3)(3m+4)=5(m+1)+8 equation: 


Simplifying
(m + -3)(3m + 4) = 5(m + 1) + 8

Reorder the terms:
(-3 + m)(3m + 4) = 5(m + 1) + 8

Reorder the terms:
(-3 + m)(4 + 3m) = 5(m + 1) + 8

Multiply (-3 + m) * (4 + 3m)
(-3(4 + 3m) + m(4 + 3m)) = 5(m + 1) + 8
((4 * -3 + 3m * -3) + m(4 + 3m)) = 5(m + 1) + 8
((-12 + -9m) + m(4 + 3m)) = 5(m + 1) + 8
(-12 + -9m + (4 * m + 3m * m)) = 5(m + 1) + 8
(-12 + -9m + (4m + 3m2)) = 5(m + 1) + 8

Combine like terms: -9m + 4m = -5m
(-12 + -5m + 3m2) = 5(m + 1) + 8

Reorder the terms:
-12 + -5m + 3m2 = 5(1 + m) + 8
-12 + -5m + 3m2 = (1 * 5 + m * 5) + 8
-12 + -5m + 3m2 = (5 + 5m) + 8

Reorder the terms:
-12 + -5m + 3m2 = 5 + 8 + 5m

Combine like terms: 5 + 8 = 13
-12 + -5m + 3m2 = 13 + 5m

Solving
-12 + -5m + 3m2 = 13 + 5m

Solving for variable 'm'.

Reorder the terms:
-12 + -13 + -5m + -5m + 3m2 = 13 + 5m + -13 + -5m

Combine like terms: -12 + -13 = -25
-25 + -5m + -5m + 3m2 = 13 + 5m + -13 + -5m

Combine like terms: -5m + -5m = -10m
-25 + -10m + 3m2 = 13 + 5m + -13 + -5m

Reorder the terms:
-25 + -10m + 3m2 = 13 + -13 + 5m + -5m

Combine like terms: 13 + -13 = 0
-25 + -10m + 3m2 = 0 + 5m + -5m
-25 + -10m + 3m2 = 5m + -5m

Combine like terms: 5m + -5m = 0
-25 + -10m + 3m2 = 0

Factor a trinomial.
(-5 + -3m)(5 + -1m) = 0


Subproblem 1
Set the factor '(-5 + -3m)' equal to zero and attempt to solve:

Simplifying
-5 + -3m = 0

Solving
-5 + -3m = 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 + -3m = 0 + 5

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

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

Divide each side by '-3'.
m = -1.666666667

Simplifying
m = -1.666666667

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

Simplifying
5 + -1m = 0

Solving
5 + -1m = 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 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Solution
m = {-1.666666667, 5}

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