a(a-3)+6-2a=0

Solution for a(a-3)+6-2a=0 equation:

Simplifying
a(a + -3) + 6 + -2a = 0

Reorder the terms:
a(-3 + a) + 6 + -2a = 0
(-3 * a + a * a) + 6 + -2a = 0
(-3a + a2) + 6 + -2a = 0

Reorder the terms:
6 + -3a + -2a + a2 = 0

Combine like terms: -3a + -2a = -5a
6 + -5a + a2 = 0

Solving
6 + -5a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
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 = {2, 3}