355*2=n(2*4+(n-1)*7)

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Solution for 355*2=n(2*4+(n-1)*7) equation: 


Simplifying
355 * 2 = n(2 * 4 + (n + -1) * 7)

Multiply 355 * 2
710 = n(2 * 4 + (n + -1) * 7)

Multiply 2 * 4
710 = n(8 + (n + -1) * 7)

Reorder the terms:
710 = n(8 + (-1 + n) * 7)

Reorder the terms for easier multiplication:
710 = n(8 + 7(-1 + n))
710 = n(8 + (-1 * 7 + n * 7))
710 = n(8 + (-7 + 7n))

Combine like terms: 8 + -7 = 1
710 = n(1 + 7n)
710 = (1 * n + 7n * n)
710 = (1n + 7n2)

Solving
710 = 1n + 7n2

Solving for variable 'n'.

Reorder the terms:
710 + -1n + -7n2 = 1n + -1n + 7n2 + -7n2

Combine like terms: 1n + -1n = 0
710 + -1n + -7n2 = 0 + 7n2 + -7n2
710 + -1n + -7n2 = 7n2 + -7n2

Combine like terms: 7n2 + -7n2 = 0
710 + -1n + -7n2 = 0

Factor a trinomial.
(10 + -1n)(71 + 7n) = 0


Subproblem 1
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10

Subproblem 2
Set the factor '(71 + 7n)' equal to zero and attempt to solve:

Simplifying
71 + 7n = 0

Solving
71 + 7n = 0

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

Add '-71' to each side of the equation.
71 + -71 + 7n = 0 + -71

Combine like terms: 71 + -71 = 0
0 + 7n = 0 + -71
7n = 0 + -71

Combine like terms: 0 + -71 = -71
7n = -71

Divide each side by '7'.
n = -10.14285714

Simplifying
n = -10.14285714
Solution
n = {10, -10.14285714}

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