(-x)(-x+1)=182

Solution for (-x)(-x+1)=182 equation:

Simplifying
(-1x)(-1x + 1) = 182

Remove parenthesis around (-1x)
-1x(-1x + 1) = 182

Reorder the terms:
-1x(1 + -1x) = 182
(1 * -1x + -1x * -1x) = 182
(-1x + 1x2) = 182

Solving
-1x + 1x2 = 182

Solving for variable 'x'.

Reorder the terms:
-182 + -1x + 1x2 = 182 + -182

Combine like terms: 182 + -182 = 0
-182 + -1x + 1x2 = 0

Factor a trinomial.
(-13 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-13, 14}