(xy+x+1)-(x+7)=0

Solution for (xy+x+1)-(x+7)=0 equation:

Simplifying
(xy + x + 1) + -1(x + 7) = 0

Reorder the terms:
(1 + x + xy) + -1(x + 7) = 0

Remove parenthesis around (1 + x + xy)
1 + x + xy + -1(x + 7) = 0

Reorder the terms:
1 + x + xy + -1(7 + x) = 0
1 + x + xy + (7 * -1 + x * -1) = 0
1 + x + xy + (-7 + -1x) = 0

Reorder the terms:
1 + -7 + x + -1x + xy = 0

Combine like terms: 1 + -7 = -6
-6 + x + -1x + xy = 0

Combine like terms: x + -1x = 0
-6 + 0 + xy = 0
-6 + xy = 0

Solving
-6 + xy = 0

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + xy = 0 + 6

Combine like terms: -6 + 6 = 0
0 + xy = 0 + 6
xy = 0 + 6

Combine like terms: 0 + 6 = 6
xy = 6

Divide each side by 'y'.
x = 6y-1

Simplifying
x = 6y-1