(2n+1)(3n+8)=(3n+4)(2n-8)

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Solution for (2n+1)(3n+8)=(3n+4)(2n-8) equation: 


Simplifying
(2n + 1)(3n + 8) = (3n + 4)(2n + -8)

Reorder the terms:
(1 + 2n)(3n + 8) = (3n + 4)(2n + -8)

Reorder the terms:
(1 + 2n)(8 + 3n) = (3n + 4)(2n + -8)

Multiply (1 + 2n) * (8 + 3n)
(1(8 + 3n) + 2n * (8 + 3n)) = (3n + 4)(2n + -8)
((8 * 1 + 3n * 1) + 2n * (8 + 3n)) = (3n + 4)(2n + -8)
((8 + 3n) + 2n * (8 + 3n)) = (3n + 4)(2n + -8)
(8 + 3n + (8 * 2n + 3n * 2n)) = (3n + 4)(2n + -8)
(8 + 3n + (16n + 6n2)) = (3n + 4)(2n + -8)

Combine like terms: 3n + 16n = 19n
(8 + 19n + 6n2) = (3n + 4)(2n + -8)

Reorder the terms:
8 + 19n + 6n2 = (4 + 3n)(2n + -8)

Reorder the terms:
8 + 19n + 6n2 = (4 + 3n)(-8 + 2n)

Multiply (4 + 3n) * (-8 + 2n)
8 + 19n + 6n2 = (4(-8 + 2n) + 3n * (-8 + 2n))
8 + 19n + 6n2 = ((-8 * 4 + 2n * 4) + 3n * (-8 + 2n))
8 + 19n + 6n2 = ((-32 + 8n) + 3n * (-8 + 2n))
8 + 19n + 6n2 = (-32 + 8n + (-8 * 3n + 2n * 3n))
8 + 19n + 6n2 = (-32 + 8n + (-24n + 6n2))

Combine like terms: 8n + -24n = -16n
8 + 19n + 6n2 = (-32 + -16n + 6n2)

Add '-6n2' to each side of the equation.
8 + 19n + 6n2 + -6n2 = -32 + -16n + 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
8 + 19n + 0 = -32 + -16n + 6n2 + -6n2
8 + 19n = -32 + -16n + 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
8 + 19n = -32 + -16n + 0
8 + 19n = -32 + -16n

Solving
8 + 19n = -32 + -16n

Solving for variable 'n'.

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

Add '16n' to each side of the equation.
8 + 19n + 16n = -32 + -16n + 16n

Combine like terms: 19n + 16n = 35n
8 + 35n = -32 + -16n + 16n

Combine like terms: -16n + 16n = 0
8 + 35n = -32 + 0
8 + 35n = -32

Add '-8' to each side of the equation.
8 + -8 + 35n = -32 + -8

Combine like terms: 8 + -8 = 0
0 + 35n = -32 + -8
35n = -32 + -8

Combine like terms: -32 + -8 = -40
35n = -40

Divide each side by '35'.
n = -1.142857143

Simplifying
n = -1.142857143

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