0=(-x-1)(x-12)

Solution for 0=(-x-1)(x-12) equation:

Simplifying
0 = (-1x + -1)(x + -12)

Reorder the terms:
0 = (-1 + -1x)(x + -12)

Reorder the terms:
0 = (-1 + -1x)(-12 + x)

Multiply (-1 + -1x) * (-12 + x)
0 = (-1(-12 + x) + -1x * (-12 + x))
0 = ((-12 * -1 + x * -1) + -1x * (-12 + x))
0 = ((12 + -1x) + -1x * (-12 + x))
0 = (12 + -1x + (-12 * -1x + x * -1x))
0 = (12 + -1x + (12x + -1x2))

Combine like terms: -1x + 12x = 11x
0 = (12 + 11x + -1x2)

Solving
0 = 12 + 11x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -11x + x2 = 12 + 11x + -1x2 + -12 + -11x + x2

Reorder the terms:
-12 + -11x + x2 = 12 + -12 + 11x + -11x + -1x2 + x2

Combine like terms: 12 + -12 = 0
-12 + -11x + x2 = 0 + 11x + -11x + -1x2 + x2
-12 + -11x + x2 = 11x + -11x + -1x2 + x2

Combine like terms: 11x + -11x = 0
-12 + -11x + x2 = 0 + -1x2 + x2
-12 + -11x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-12 + -11x + x2 = 0

Factor a trinomial.
(-1 + -1x)(12 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-1, 12}