x(p+q+1)=1

Solution for x(p+q+1)=1 equation:

Simplifying
x(p + q + 1) = 1

Reorder the terms:
x(1 + p + q) = 1
(1 * x + p * x + q * x) = 1

Reorder the terms:
(px + qx + 1x) = 1
(px + qx + 1x) = 1

Solving
px + qx + 1x = 1

Solving for variable 'p'.

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

Add '-1qx' to each side of the equation.
px + qx + -1qx + 1x = 1 + -1qx

Combine like terms: qx + -1qx = 0
px + 0 + 1x = 1 + -1qx
px + 1x = 1 + -1qx

Add '-1x' to each side of the equation.
px + 1x + -1x = 1 + -1qx + -1x

Combine like terms: 1x + -1x = 0
px + 0 = 1 + -1qx + -1x
px = 1 + -1qx + -1x

Divide each side by 'x'.
p = x-1 + -1q + -1

Simplifying
p = x-1 + -1q + -1

Reorder the terms:
p = -1 + -1q + x-1