x^2-x+7=9x-2

Solution for x^2-x+7=9x-2 equation:

Simplifying
x2 + -1x + 7 = 9x + -2

Reorder the terms:
7 + -1x + x2 = 9x + -2

Reorder the terms:
7 + -1x + x2 = -2 + 9x

Solving
7 + -1x + x2 = -2 + 9x

Solving for variable 'x'.

Reorder the terms:
7 + 2 + -1x + -9x + x2 = -2 + 9x + 2 + -9x

Combine like terms: 7 + 2 = 9
9 + -1x + -9x + x2 = -2 + 9x + 2 + -9x

Combine like terms: -1x + -9x = -10x
9 + -10x + x2 = -2 + 9x + 2 + -9x

Reorder the terms:
9 + -10x + x2 = -2 + 2 + 9x + -9x

Combine like terms: -2 + 2 = 0
9 + -10x + x2 = 0 + 9x + -9x
9 + -10x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
9 + -10x + 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}