3x^2-2x+3=x-3

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

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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
6 + -3x + 3x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
6 + -3x + 3x2 = 0 + x + -1x
6 + -3x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
6 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x + x2 = 0

Solving
2 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1x + x2 = 0 + -2

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

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -2 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1x + x2 = -1.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.