(4z-5)(3+z)=0

Solution for (4z-5)(3+z)=0 equation:

Simplifying
(4z + -5)(3 + z) = 0

Reorder the terms:
(-5 + 4z)(3 + z) = 0

Multiply (-5 + 4z) * (3 + z)
(-5(3 + z) + 4z * (3 + z)) = 0
((3 * -5 + z * -5) + 4z * (3 + z)) = 0
((-15 + -5z) + 4z * (3 + z)) = 0
(-15 + -5z + (3 * 4z + z * 4z)) = 0
(-15 + -5z + (12z + 4z2)) = 0

Combine like terms: -5z + 12z = 7z
(-15 + 7z + 4z2) = 0

Solving
-15 + 7z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(5 + -4z) = 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 '(5 + -4z)' equal to zero and attempt to solve:

Simplifying
5 + -4z = 0

Solving
5 + -4z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z = 0 + -5
-4z = 0 + -5

Combine like terms: 0 + -5 = -5
-4z = -5

Divide each side by '-4'.
z = 1.25

Simplifying
z = 1.25
Solution
z = {-3, 1.25}