(a-3)(a-4)=0

Solution for (a-3)(a-4)=0 equation:

Simplifying
(a + -3)(a + -4) = 0

Reorder the terms:
(-3 + a)(a + -4) = 0

Reorder the terms:
(-3 + a)(-4 + a) = 0

Multiply (-3 + a) * (-4 + a)
(-3(-4 + a) + a(-4 + a)) = 0
((-4 * -3 + a * -3) + a(-4 + a)) = 0
((12 + -3a) + a(-4 + a)) = 0
(12 + -3a + (-4 * a + a * a)) = 0
(12 + -3a + (-4a + a2)) = 0

Combine like terms: -3a + -4a = -7a
(12 + -7a + a2) = 0

Solving
12 + -7a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -1a)(4 + -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 '(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 = {3, 4}