n(n+40)+28=(n-1)(n+8)

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Solution for n(n+40)+28=(n-1)(n+8) equation: 


Simplifying
n(n + 40) + 28 = (n + -1)(n + 8)

Reorder the terms:
n(40 + n) + 28 = (n + -1)(n + 8)
(40 * n + n * n) + 28 = (n + -1)(n + 8)
(40n + n2) + 28 = (n + -1)(n + 8)

Reorder the terms:
28 + 40n + n2 = (n + -1)(n + 8)

Reorder the terms:
28 + 40n + n2 = (-1 + n)(n + 8)

Reorder the terms:
28 + 40n + n2 = (-1 + n)(8 + n)

Multiply (-1 + n) * (8 + n)
28 + 40n + n2 = (-1(8 + n) + n(8 + n))
28 + 40n + n2 = ((8 * -1 + n * -1) + n(8 + n))
28 + 40n + n2 = ((-8 + -1n) + n(8 + n))
28 + 40n + n2 = (-8 + -1n + (8 * n + n * n))
28 + 40n + n2 = (-8 + -1n + (8n + n2))

Combine like terms: -1n + 8n = 7n
28 + 40n + n2 = (-8 + 7n + n2)

Add '-1n2' to each side of the equation.
28 + 40n + n2 + -1n2 = -8 + 7n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
28 + 40n + 0 = -8 + 7n + n2 + -1n2
28 + 40n = -8 + 7n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
28 + 40n = -8 + 7n + 0
28 + 40n = -8 + 7n

Solving
28 + 40n = -8 + 7n

Solving for variable 'n'.

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

Add '-7n' to each side of the equation.
28 + 40n + -7n = -8 + 7n + -7n

Combine like terms: 40n + -7n = 33n
28 + 33n = -8 + 7n + -7n

Combine like terms: 7n + -7n = 0
28 + 33n = -8 + 0
28 + 33n = -8

Add '-28' to each side of the equation.
28 + -28 + 33n = -8 + -28

Combine like terms: 28 + -28 = 0
0 + 33n = -8 + -28
33n = -8 + -28

Combine like terms: -8 + -28 = -36
33n = -36

Divide each side by '33'.
n = -1.090909091

Simplifying
n = -1.090909091

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