x(x+17)-10(x+17)=0

Solution for x(x+17)-10(x+17)=0 equation:

Simplifying
x(x + 17) + -10(x + 17) = 0

Reorder the terms:
x(17 + x) + -10(x + 17) = 0
(17 * x + x * x) + -10(x + 17) = 0
(17x + x2) + -10(x + 17) = 0

Reorder the terms:
17x + x2 + -10(17 + x) = 0
17x + x2 + (17 * -10 + x * -10) = 0
17x + x2 + (-170 + -10x) = 0

Reorder the terms:
-170 + 17x + -10x + x2 = 0

Combine like terms: 17x + -10x = 7x
-170 + 7x + x2 = 0

Solving
-170 + 7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-17, 10}