(-17+-1x)(2+-1x)=0

Solution for (-17+-1x)(2+-1x)=0 equation:

Simplifying
(-17 + -1x)(2 + -1x) = 0

Multiply (-17 + -1x) * (2 + -1x)
(-17(2 + -1x) + -1x * (2 + -1x)) = 0
((2 * -17 + -1x * -17) + -1x * (2 + -1x)) = 0
((-34 + 17x) + -1x * (2 + -1x)) = 0
(-34 + 17x + (2 * -1x + -1x * -1x)) = 0
(-34 + 17x + (-2x + 1x2)) = 0

Combine like terms: 17x + -2x = 15x
(-34 + 15x + 1x2) = 0

Solving
-34 + 15x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-17, 2}