3x+7=x^2-2x+1

Solution for 3x+7=x^2-2x+1 equation:

Simplifying
3x + 7 = x2 + -2x + 1

Reorder the terms:
7 + 3x = x2 + -2x + 1

Reorder the terms:
7 + 3x = 1 + -2x + x2

Solving
7 + 3x = 1 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -1 + 3x + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 7 + -1 = 6
6 + 3x + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 3x + 2x = 5x
6 + 5x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Reorder the terms:
6 + 5x + -1x2 = 1 + -1 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
6 + 5x + -1x2 = 0 + -2x + 2x + x2 + -1x2
6 + 5x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
6 + 5x + -1x2 = 0 + x2 + -1x2
6 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(1 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {6, -1}