a^2=6a-9

Solution for a^2=6a-9 equation:

Simplifying
a2 = 6a + -9

Reorder the terms:
a2 = -9 + 6a

Solving
a2 = -9 + 6a

Solving for variable 'a'.

Reorder the terms:
9 + -6a + a2 = -9 + 6a + 9 + -6a

Reorder the terms:
9 + -6a + a2 = -9 + 9 + 6a + -6a

Combine like terms: -9 + 9 = 0
9 + -6a + a2 = 0 + 6a + -6a
9 + -6a + a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
9 + -6a + a2 = 0

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

Subproblem 1
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
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 = {3, 3}