In(x-4)+in(x+1)=in(x+8)

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Solution for In(x-4)+in(x+1)=in(x+8) equation: 


Simplifying
In(x + -4) + in(x + 1) = in(x + 8)

Reorder the terms:
nI(-4 + x) + in(x + 1) = in(x + 8)
(-4 * nI + x * nI) + in(x + 1) = in(x + 8)
(-4nI + nxI) + in(x + 1) = in(x + 8)

Reorder the terms:
-4nI + nxI + in(1 + x) = in(x + 8)
-4nI + nxI + (1 * in + x * in) = in(x + 8)
-4nI + nxI + (1in + inx) = in(x + 8)

Reorder the terms:
1in + inx + -4nI + nxI = in(x + 8)

Reorder the terms:
1in + inx + -4nI + nxI = in(8 + x)
1in + inx + -4nI + nxI = (8 * in + x * in)
1in + inx + -4nI + nxI = (8in + inx)

Add '-1inx' to each side of the equation.
1in + inx + -4nI + -1inx + nxI = 8in + inx + -1inx

Reorder the terms:
1in + inx + -1inx + -4nI + nxI = 8in + inx + -1inx

Combine like terms: inx + -1inx = 0
1in + 0 + -4nI + nxI = 8in + inx + -1inx
1in + -4nI + nxI = 8in + inx + -1inx

Combine like terms: inx + -1inx = 0
1in + -4nI + nxI = 8in + 0
1in + -4nI + nxI = 8in

Solving
1in + -4nI + nxI = 8in

Solving for variable 'i'.

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

Add '-8in' to each side of the equation.
1in + -4nI + -8in + nxI = 8in + -8in

Reorder the terms:
1in + -8in + -4nI + nxI = 8in + -8in

Combine like terms: 1in + -8in = -7in
-7in + -4nI + nxI = 8in + -8in

Combine like terms: 8in + -8in = 0
-7in + -4nI + nxI = 0

Add '4nI' to each side of the equation.
-7in + -4nI + 4nI + nxI = 0 + 4nI

Combine like terms: -4nI + 4nI = 0
-7in + 0 + nxI = 0 + 4nI
-7in + nxI = 0 + 4nI
Remove the zero:
-7in + nxI = 4nI

Add '-1nxI' to each side of the equation.
-7in + nxI + -1nxI = 4nI + -1nxI

Combine like terms: nxI + -1nxI = 0
-7in + 0 = 4nI + -1nxI
-7in = 4nI + -1nxI

Divide each side by '-7n'.
i = -0.5714285714I + 0.1428571429xI

Simplifying
i = -0.5714285714I + 0.1428571429xI

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