(x+1)(z+1)=(y-1)(y+6)

Solution for (x+1)(z+1)=(y-1)(y+6) equation:

Simplifying
(x + 1)(z + 1) = (y + -1)(y + 6)

Reorder the terms:
(1 + x)(z + 1) = (y + -1)(y + 6)

Reorder the terms:
(1 + x)(1 + z) = (y + -1)(y + 6)

Multiply (1 + x) * (1 + z)
(1(1 + z) + x(1 + z)) = (y + -1)(y + 6)
((1 * 1 + z * 1) + x(1 + z)) = (y + -1)(y + 6)
((1 + 1z) + x(1 + z)) = (y + -1)(y + 6)
(1 + 1z + (1 * x + z * x)) = (y + -1)(y + 6)
(1 + 1z + (1x + xz)) = (y + -1)(y + 6)

Reorder the terms:
(1 + 1x + xz + 1z) = (y + -1)(y + 6)
(1 + 1x + xz + 1z) = (y + -1)(y + 6)

Reorder the terms:
1 + 1x + xz + 1z = (-1 + y)(y + 6)

Reorder the terms:
1 + 1x + xz + 1z = (-1 + y)(6 + y)

Multiply (-1 + y) * (6 + y)
1 + 1x + xz + 1z = (-1(6 + y) + y(6 + y))
1 + 1x + xz + 1z = ((6 * -1 + y * -1) + y(6 + y))
1 + 1x + xz + 1z = ((-6 + -1y) + y(6 + y))
1 + 1x + xz + 1z = (-6 + -1y + (6 * y + y * y))
1 + 1x + xz + 1z = (-6 + -1y + (6y + y2))

Combine like terms: -1y + 6y = 5y
1 + 1x + xz + 1z = (-6 + 5y + y2)

Solving
1 + 1x + xz + 1z = -6 + 5y + y2

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + 1x + xz + -1 + 1z = -6 + 5y + -1 + y2

Reorder the terms:
1 + -1 + 1x + xz + 1z = -6 + 5y + -1 + y2

Combine like terms: 1 + -1 = 0
0 + 1x + xz + 1z = -6 + 5y + -1 + y2
1x + xz + 1z = -6 + 5y + -1 + y2

Reorder the terms:
1x + xz + 1z = -6 + -1 + 5y + y2

Combine like terms: -6 + -1 = -7
1x + xz + 1z = -7 + 5y + y2

Add '-1z' to each side of the equation.
1x + xz + 1z + -1z = -7 + 5y + y2 + -1z

Combine like terms: 1z + -1z = 0
1x + xz + 0 = -7 + 5y + y2 + -1z
1x + xz = -7 + 5y + y2 + -1z

Reorder the terms:
7 + 1x + xz + -5y + -1y2 + z = -7 + 5y + y2 + -1z + 7 + -5y + -1y2 + z

Reorder the terms:
7 + 1x + xz + -5y + -1y2 + z = -7 + 7 + 5y + -5y + y2 + -1y2 + -1z + z

Combine like terms: -7 + 7 = 0
7 + 1x + xz + -5y + -1y2 + z = 0 + 5y + -5y + y2 + -1y2 + -1z + z
7 + 1x + xz + -5y + -1y2 + z = 5y + -5y + y2 + -1y2 + -1z + z

Combine like terms: 5y + -5y = 0
7 + 1x + xz + -5y + -1y2 + z = 0 + y2 + -1y2 + -1z + z
7 + 1x + xz + -5y + -1y2 + z = y2 + -1y2 + -1z + z

Combine like terms: y2 + -1y2 = 0
7 + 1x + xz + -5y + -1y2 + z = 0 + -1z + z
7 + 1x + xz + -5y + -1y2 + z = -1z + z

Combine like terms: -1z + z = 0
7 + 1x + xz + -5y + -1y2 + z = 0

The solution to this equation could not be determined.