89-9x=98-x^2-x

Solution for 89-9x=98-x^2-x equation:

Simplifying
89 + -9x = 98 + -1x2 + -1x

Reorder the terms:
89 + -9x = 98 + -1x + -1x2

Solving
89 + -9x = 98 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
89 + -98 + -9x + x + x2 = 98 + -1x + -1x2 + -98 + x + x2

Combine like terms: 89 + -98 = -9
-9 + -9x + x + x2 = 98 + -1x + -1x2 + -98 + x + x2

Combine like terms: -9x + x = -8x
-9 + -8x + x2 = 98 + -1x + -1x2 + -98 + x + x2

Reorder the terms:
-9 + -8x + x2 = 98 + -98 + -1x + x + -1x2 + x2

Combine like terms: 98 + -98 = 0
-9 + -8x + x2 = 0 + -1x + x + -1x2 + x2
-9 + -8x + x2 = -1x + x + -1x2 + x2

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

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

Factor a trinomial.
(-1 + -1x)(9 + -1x) = 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 + -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
Solution
x = {-1, 9}