log(x+1)(a+x-6)=2

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Solution for log(x+1)(a+x-6)=2 equation: 


Simplifying
log(x + 1)(a + x + -6) = 2

Reorder the terms:
glo(1 + x)(a + x + -6) = 2

Reorder the terms:
glo(1 + x)(-6 + a + x) = 2

Multiply (1 + x) * (-6 + a + x)
glo(1(-6 + a + x) + x(-6 + a + x)) = 2
glo((-6 * 1 + a * 1 + x * 1) + x(-6 + a + x)) = 2
glo((-6 + 1a + 1x) + x(-6 + a + x)) = 2
glo(-6 + 1a + 1x + (-6 * x + a * x + x * x)) = 2

Reorder the terms:
glo(-6 + 1a + 1x + (ax + -6x + x2)) = 2
glo(-6 + 1a + 1x + (ax + -6x + x2)) = 2

Reorder the terms:
glo(-6 + 1a + ax + 1x + -6x + x2) = 2

Combine like terms: 1x + -6x = -5x
glo(-6 + 1a + ax + -5x + x2) = 2
(-6 * glo + 1a * glo + ax * glo + -5x * glo + x2 * glo) = 2

Reorder the terms:
(1aglo + aglox + -6glo + -5glox + glox2) = 2
(1aglo + aglox + -6glo + -5glox + glox2) = 2

Solving
1aglo + aglox + -6glo + -5glox + glox2 = 2

Solving for variable 'a'.

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

Add '6glo' to each side of the equation.
1aglo + aglox + -6glo + -5glox + 6glo + glox2 = 2 + 6glo

Reorder the terms:
1aglo + aglox + -6glo + 6glo + -5glox + glox2 = 2 + 6glo

Combine like terms: -6glo + 6glo = 0
1aglo + aglox + 0 + -5glox + glox2 = 2 + 6glo
1aglo + aglox + -5glox + glox2 = 2 + 6glo

Add '5glox' to each side of the equation.
1aglo + aglox + -5glox + 5glox + glox2 = 2 + 6glo + 5glox

Combine like terms: -5glox + 5glox = 0
1aglo + aglox + 0 + glox2 = 2 + 6glo + 5glox
1aglo + aglox + glox2 = 2 + 6glo + 5glox

Add '-1glox2' to each side of the equation.
1aglo + aglox + glox2 + -1glox2 = 2 + 6glo + 5glox + -1glox2

Combine like terms: glox2 + -1glox2 = 0
1aglo + aglox + 0 = 2 + 6glo + 5glox + -1glox2
1aglo + aglox = 2 + 6glo + 5glox + -1glox2

Reorder the terms:
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 2 + 6glo + 5glox + -1glox2 + -2 + -6glo + -5glox + glox2

Reorder the terms:
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 2 + -2 + 6glo + -6glo + 5glox + -5glox + -1glox2 + glox2

Combine like terms: 2 + -2 = 0
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 0 + 6glo + -6glo + 5glox + -5glox + -1glox2 + glox2
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 6glo + -6glo + 5glox + -5glox + -1glox2 + glox2

Combine like terms: 6glo + -6glo = 0
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 0 + 5glox + -5glox + -1glox2 + glox2
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 5glox + -5glox + -1glox2 + glox2

Combine like terms: 5glox + -5glox = 0
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 0 + -1glox2 + glox2
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = -1glox2 + glox2

Combine like terms: -1glox2 + glox2 = 0
-2 + 1aglo + aglox + -6glo + -5glox + glox2 = 0

The solution to this equation could not be determined.

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