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

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

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

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

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

Multiply (-9 + x) * (1 + x)
0 = (-9(1 + x) + x(1 + x))
0 = ((1 * -9 + x * -9) + x(1 + x))
0 = ((-9 + -9x) + x(1 + x))
0 = (-9 + -9x + (1 * x + x * x))
0 = (-9 + -9x + (1x + x2))

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

Solving
0 = -9 + -8x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(9 + -1x)(1 + x) = 0

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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