3x^2-5x+7=x^2+2x+1

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Solution for 3x^2-5x+7=x^2+2x+1 equation: 


Simplifying
3x2 + -5x + 7 = x2 + 2x + 1

Reorder the terms:
7 + -5x + 3x2 = x2 + 2x + 1

Reorder the terms:
7 + -5x + 3x2 = 1 + 2x + x2

Solving
7 + -5x + 3x2 = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -1 + -5x + -2x + 3x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 7 + -1 = 6
6 + -5x + -2x + 3x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -5x + -2x = -7x
6 + -7x + 3x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

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

Reorder the terms:
6 + -7x + 2x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
6 + -7x + 2x2 = 0 + 2x + -2x + x2 + -1x2
6 + -7x + 2x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
6 + -7x + 2x2 = 0 + x2 + -1x2
6 + -7x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -7x + 2x2 = 0

Factor a trinomial.
(3 + -2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, 2}

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