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

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

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

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

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

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

Combine like terms: -4a + -3a = -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}