5n+7+n=3n-2+4n(2n+1)

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Solution for 5n+7+n=3n-2+4n(2n+1) equation: 


Simplifying
5n + 7 + n = 3n + -2 + 4n(2n + 1)

Reorder the terms:
7 + 5n + n = 3n + -2 + 4n(2n + 1)

Combine like terms: 5n + n = 6n
7 + 6n = 3n + -2 + 4n(2n + 1)

Reorder the terms:
7 + 6n = 3n + -2 + 4n(1 + 2n)
7 + 6n = 3n + -2 + (1 * 4n + 2n * 4n)
7 + 6n = 3n + -2 + (4n + 8n2)

Reorder the terms:
7 + 6n = -2 + 3n + 4n + 8n2

Combine like terms: 3n + 4n = 7n
7 + 6n = -2 + 7n + 8n2

Solving
7 + 6n = -2 + 7n + 8n2

Solving for variable 'n'.

Reorder the terms:
7 + 2 + 6n + -7n + -8n2 = -2 + 7n + 8n2 + 2 + -7n + -8n2

Combine like terms: 7 + 2 = 9
9 + 6n + -7n + -8n2 = -2 + 7n + 8n2 + 2 + -7n + -8n2

Combine like terms: 6n + -7n = -1n
9 + -1n + -8n2 = -2 + 7n + 8n2 + 2 + -7n + -8n2

Reorder the terms:
9 + -1n + -8n2 = -2 + 2 + 7n + -7n + 8n2 + -8n2

Combine like terms: -2 + 2 = 0
9 + -1n + -8n2 = 0 + 7n + -7n + 8n2 + -8n2
9 + -1n + -8n2 = 7n + -7n + 8n2 + -8n2

Combine like terms: 7n + -7n = 0
9 + -1n + -8n2 = 0 + 8n2 + -8n2
9 + -1n + -8n2 = 8n2 + -8n2

Combine like terms: 8n2 + -8n2 = 0
9 + -1n + -8n2 = 0

Factor a trinomial.
(1 + -1n)(9 + 8n) = 0


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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1

Subproblem 2
Set the factor '(9 + 8n)' equal to zero and attempt to solve:

Simplifying
9 + 8n = 0

Solving
9 + 8n = 0

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

Add '-9' to each side of the equation.
9 + -9 + 8n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8n = 0 + -9
8n = 0 + -9

Combine like terms: 0 + -9 = -9
8n = -9

Divide each side by '8'.
n = -1.125

Simplifying
n = -1.125
Solution
n = {1, -1.125}

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