(a-3)(a-3)=1

Solution for (a-3)(a-3)=1 equation:

Simplifying
(a + -3)(a + -3) = 1

Reorder the terms:
(-3 + a)(a + -3) = 1

Reorder the terms:
(-3 + a)(-3 + a) = 1

Multiply (-3 + a) * (-3 + a)
(-3(-3 + a) + a(-3 + a)) = 1
((-3 * -3 + a * -3) + a(-3 + a)) = 1
((9 + -3a) + a(-3 + a)) = 1
(9 + -3a + (-3 * a + a * a)) = 1
(9 + -3a + (-3a + a2)) = 1

Combine like terms: -3a + -3a = -6a
(9 + -6a + a2) = 1

Solving
9 + -6a + a2 = 1

Solving for variable 'a'.

Reorder the terms:
9 + -1 + -6a + a2 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + -6a + a2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -6a + a2 = 0

Factor a trinomial.
(2 + -1a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {2, 4}