(m+3)(5m+1)=(2m+1)(m+7)

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Solution for (m+3)(5m+1)=(2m+1)(m+7) equation: 


Simplifying
(m + 3)(5m + 1) = (2m + 1)(m + 7)

Reorder the terms:
(3 + m)(5m + 1) = (2m + 1)(m + 7)

Reorder the terms:
(3 + m)(1 + 5m) = (2m + 1)(m + 7)

Multiply (3 + m) * (1 + 5m)
(3(1 + 5m) + m(1 + 5m)) = (2m + 1)(m + 7)
((1 * 3 + 5m * 3) + m(1 + 5m)) = (2m + 1)(m + 7)
((3 + 15m) + m(1 + 5m)) = (2m + 1)(m + 7)
(3 + 15m + (1 * m + 5m * m)) = (2m + 1)(m + 7)
(3 + 15m + (1m + 5m2)) = (2m + 1)(m + 7)

Combine like terms: 15m + 1m = 16m
(3 + 16m + 5m2) = (2m + 1)(m + 7)

Reorder the terms:
3 + 16m + 5m2 = (1 + 2m)(m + 7)

Reorder the terms:
3 + 16m + 5m2 = (1 + 2m)(7 + m)

Multiply (1 + 2m) * (7 + m)
3 + 16m + 5m2 = (1(7 + m) + 2m * (7 + m))
3 + 16m + 5m2 = ((7 * 1 + m * 1) + 2m * (7 + m))
3 + 16m + 5m2 = ((7 + 1m) + 2m * (7 + m))
3 + 16m + 5m2 = (7 + 1m + (7 * 2m + m * 2m))
3 + 16m + 5m2 = (7 + 1m + (14m + 2m2))

Combine like terms: 1m + 14m = 15m
3 + 16m + 5m2 = (7 + 15m + 2m2)

Solving
3 + 16m + 5m2 = 7 + 15m + 2m2

Solving for variable 'm'.

Reorder the terms:
3 + -7 + 16m + -15m + 5m2 + -2m2 = 7 + 15m + 2m2 + -7 + -15m + -2m2

Combine like terms: 3 + -7 = -4
-4 + 16m + -15m + 5m2 + -2m2 = 7 + 15m + 2m2 + -7 + -15m + -2m2

Combine like terms: 16m + -15m = 1m
-4 + 1m + 5m2 + -2m2 = 7 + 15m + 2m2 + -7 + -15m + -2m2

Combine like terms: 5m2 + -2m2 = 3m2
-4 + 1m + 3m2 = 7 + 15m + 2m2 + -7 + -15m + -2m2

Reorder the terms:
-4 + 1m + 3m2 = 7 + -7 + 15m + -15m + 2m2 + -2m2

Combine like terms: 7 + -7 = 0
-4 + 1m + 3m2 = 0 + 15m + -15m + 2m2 + -2m2
-4 + 1m + 3m2 = 15m + -15m + 2m2 + -2m2

Combine like terms: 15m + -15m = 0
-4 + 1m + 3m2 = 0 + 2m2 + -2m2
-4 + 1m + 3m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
-4 + 1m + 3m2 = 0

Factor a trinomial.
(-4 + -3m)(1 + -1m) = 0


Subproblem 1
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

Subproblem 2
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
Solution
m = {-1.333333333, 1}

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