x^2-2x+5=9x-5

Solution for x^2-2x+5=9x-5 equation:

Simplifying
x2 + -2x + 5 = 9x + -5

Reorder the terms:
5 + -2x + x2 = 9x + -5

Reorder the terms:
5 + -2x + x2 = -5 + 9x

Solving
5 + -2x + x2 = -5 + 9x

Solving for variable 'x'.

Reorder the terms:
5 + 5 + -2x + -9x + x2 = -5 + 9x + 5 + -9x

Combine like terms: 5 + 5 = 10
10 + -2x + -9x + x2 = -5 + 9x + 5 + -9x

Combine like terms: -2x + -9x = -11x
10 + -11x + x2 = -5 + 9x + 5 + -9x

Reorder the terms:
10 + -11x + x2 = -5 + 5 + 9x + -9x

Combine like terms: -5 + 5 = 0
10 + -11x + x2 = 0 + 9x + -9x
10 + -11x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
10 + -11x + x2 = 0

Factor a trinomial.
(1 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {1, 10}