x^2-2x+3=4x-6

Solution for x^2-2x+3=4x-6 equation:

Simplifying
x2 + -2x + 3 = 4x + -6

Reorder the terms:
3 + -2x + x2 = 4x + -6

Reorder the terms:
3 + -2x + x2 = -6 + 4x

Solving
3 + -2x + x2 = -6 + 4x

Solving for variable 'x'.

Reorder the terms:
3 + 6 + -2x + -4x + x2 = -6 + 4x + 6 + -4x

Combine like terms: 3 + 6 = 9
9 + -2x + -4x + x2 = -6 + 4x + 6 + -4x

Combine like terms: -2x + -4x = -6x
9 + -6x + x2 = -6 + 4x + 6 + -4x

Reorder the terms:
9 + -6x + x2 = -6 + 6 + 4x + -4x

Combine like terms: -6 + 6 = 0
9 + -6x + x2 = 0 + 4x + -4x
9 + -6x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
9 + -6x + x2 = 0

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}