(z-3)(z-4)=0

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

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

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

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

Multiply (-3 + z) * (-4 + z)
(-3(-4 + z) + z(-4 + z)) = 0
((-4 * -3 + z * -3) + z(-4 + z)) = 0
((12 + -3z) + z(-4 + z)) = 0
(12 + -3z + (-4 * z + z * z)) = 0
(12 + -3z + (-4z + z2)) = 0

Combine like terms: -3z + -4z = -7z
(12 + -7z + z2) = 0

Solving
12 + -7z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(4 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

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

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

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

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

Simplifying
z = 4
Solution
z = {3, 4}