(3-z)(4z-1)=0

Solution for (3-z)(4z-1)=0 equation:

Simplifying
(3 + -1z)(4z + -1) = 0

Reorder the terms:
(3 + -1z)(-1 + 4z) = 0

Multiply (3 + -1z) * (-1 + 4z)
(3(-1 + 4z) + -1z * (-1 + 4z)) = 0
((-1 * 3 + 4z * 3) + -1z * (-1 + 4z)) = 0
((-3 + 12z) + -1z * (-1 + 4z)) = 0
(-3 + 12z + (-1 * -1z + 4z * -1z)) = 0
(-3 + 12z + (1z + -4z2)) = 0

Combine like terms: 12z + 1z = 13z
(-3 + 13z + -4z2) = 0

Solving
-3 + 13z + -4z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-3 + z = 0

Solving
-3 + z = 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 + z = 0 + 3

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

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

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

Simplifying
1 + -4z = 0

Solving
1 + -4z = 0

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

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

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

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

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Solution
z = {3, 0.25}