-(x-1)x-9(x-1)=0

Solution for -(x-1)x-9(x-1)=0 equation:

Simplifying
-1(x + -1) * x + -9(x + -1) = 0

Reorder the terms:
-1(-1 + x) * x + -9(x + -1) = 0

Reorder the terms for easier multiplication:
-1x(-1 + x) + -9(x + -1) = 0
(-1 * -1x + x * -1x) + -9(x + -1) = 0
(1x + -1x2) + -9(x + -1) = 0

Reorder the terms:
1x + -1x2 + -9(-1 + x) = 0
1x + -1x2 + (-1 * -9 + x * -9) = 0
1x + -1x2 + (9 + -9x) = 0

Reorder the terms:
9 + 1x + -9x + -1x2 = 0

Combine like terms: 1x + -9x = -8x
9 + -8x + -1x2 = 0

Solving
9 + -8x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(9 + x) = 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 '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {1, -9}