(a-3)(a-4)=2

Solution for (a-3)(a-4)=2 equation:

Simplifying
(a + -3)(a + -4) = 2

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

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

Multiply (-3 + a) * (-4 + a)
(-3(-4 + a) + a(-4 + a)) = 2
((-4 * -3 + a * -3) + a(-4 + a)) = 2
((12 + -3a) + a(-4 + a)) = 2
(12 + -3a + (-4 * a + a * a)) = 2
(12 + -3a + (-4a + a2)) = 2

Combine like terms: -3a + -4a = -7a
(12 + -7a + a2) = 2

Solving
12 + -7a + a2 = 2

Solving for variable 'a'.

Reorder the terms:
12 + -2 + -7a + a2 = 2 + -2

Combine like terms: 12 + -2 = 10
10 + -7a + a2 = 2 + -2

Combine like terms: 2 + -2 = 0
10 + -7a + a2 = 0

Factor a trinomial.
(2 + -1a)(5 + -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 '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {2, 5}