x(x+1)-(x+(x+1))=71

Solution for x(x+1)-(x+(x+1))=71 equation:

Simplifying
x(x + 1) + -1(x + (x + 1)) = 71

Reorder the terms:
x(1 + x) + -1(x + (x + 1)) = 71
(1 * x + x * x) + -1(x + (x + 1)) = 71
(1x + x2) + -1(x + (x + 1)) = 71

Reorder the terms:
1x + x2 + -1(x + (1 + x)) = 71

Remove parenthesis around (1 + x)
1x + x2 + -1(x + 1 + x) = 71

Reorder the terms:
1x + x2 + -1(1 + x + x) = 71

Combine like terms: x + x = 2x
1x + x2 + -1(1 + 2x) = 71
1x + x2 + (1 * -1 + 2x * -1) = 71
1x + x2 + (-1 + -2x) = 71

Reorder the terms:
-1 + 1x + -2x + x2 = 71

Combine like terms: 1x + -2x = -1x
-1 + -1x + x2 = 71

Solving
-1 + -1x + x2 = 71

Solving for variable 'x'.

Reorder the terms:
-1 + -71 + -1x + x2 = 71 + -71

Combine like terms: -1 + -71 = -72
-72 + -1x + x2 = 71 + -71

Combine like terms: 71 + -71 = 0
-72 + -1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-8, 9}