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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Reorder the terms:
9 + -8x + -1x2 = -9 + 9 + 9x + -9x

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

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

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}