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

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

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

Reorder the terms:
(-2 + a)(a + 2) = 3(a + -2)

Reorder the terms:
(-2 + a)(2 + a) = 3(a + -2)

Multiply (-2 + a) * (2 + a)
(-2(2 + a) + a(2 + a)) = 3(a + -2)
((2 * -2 + a * -2) + a(2 + a)) = 3(a + -2)
((-4 + -2a) + a(2 + a)) = 3(a + -2)
(-4 + -2a + (2 * a + a * a)) = 3(a + -2)
(-4 + -2a + (2a + a2)) = 3(a + -2)

Combine like terms: -2a + 2a = 0
(-4 + 0 + a2) = 3(a + -2)
(-4 + a2) = 3(a + -2)

Reorder the terms:
-4 + a2 = 3(-2 + a)
-4 + a2 = (-2 * 3 + a * 3)
-4 + a2 = (-6 + 3a)

Solving
-4 + a2 = -6 + 3a

Solving for variable 'a'.

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

Combine like terms: -4 + 6 = 2
2 + -3a + a2 = -6 + 3a + 6 + -3a

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

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

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

Factor a trinomial.
(1 + -1a)(2 + -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 '(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
Solution
a = {1, 2}