x(x-17)-8(x-17)=0

Solution for x(x-17)-8(x-17)=0 equation:

Simplifying
x(x + -17) + -8(x + -17) = 0

Reorder the terms:
x(-17 + x) + -8(x + -17) = 0
(-17 * x + x * x) + -8(x + -17) = 0
(-17x + x2) + -8(x + -17) = 0

Reorder the terms:
-17x + x2 + -8(-17 + x) = 0
-17x + x2 + (-17 * -8 + x * -8) = 0
-17x + x2 + (136 + -8x) = 0

Reorder the terms:
136 + -17x + -8x + x2 = 0

Combine like terms: -17x + -8x = -25x
136 + -25x + x2 = 0

Solving
136 + -25x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -1x)(17 + -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 '(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
Solution
x = {8, 17}