1-x^2+6x-9=0

Solution for 1-x^2+6x-9=0 equation:

Simplifying
1 + -1x2 + 6x + -9 = 0

Reorder the terms:
1 + -9 + 6x + -1x2 = 0

Combine like terms: 1 + -9 = -8
-8 + 6x + -1x2 = 0

Solving
-8 + 6x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {4, 2}