x+x^2-6x+7=3

Solution for x+x^2-6x+7=3 equation:

Simplifying
x + x2 + -6x + 7 = 3

Reorder the terms:
7 + x + -6x + x2 = 3

Combine like terms: x + -6x = -5x
7 + -5x + x2 = 3

Solving
7 + -5x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
7 + -3 + -5x + x2 = 3 + -3

Combine like terms: 7 + -3 = 4
4 + -5x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
4 + -5x + x2 = 0

Factor a trinomial.
(1 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}