a^2-4a+6=3

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

Simplifying
a2 + -4a + 6 = 3

Reorder the terms:
6 + -4a + a2 = 3

Solving
6 + -4a + a2 = 3

Solving for variable 'a'.

Reorder the terms:
6 + -3 + -4a + a2 = 3 + -3

Combine like terms: 6 + -3 = 3
3 + -4a + a2 = 3 + -3

Combine like terms: 3 + -3 = 0
3 + -4a + a2 = 0

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 1

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

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

Simplifying
a = 3
Solution
a = {1, 3}