(2z-7)(4+z)=0

Solution for (2z-7)(4+z)=0 equation:

Simplifying
(2z + -7)(4 + z) = 0

Reorder the terms:
(-7 + 2z)(4 + z) = 0

Multiply (-7 + 2z) * (4 + z)
(-7(4 + z) + 2z * (4 + z)) = 0
((4 * -7 + z * -7) + 2z * (4 + z)) = 0
((-28 + -7z) + 2z * (4 + z)) = 0
(-28 + -7z + (4 * 2z + z * 2z)) = 0
(-28 + -7z + (8z + 2z2)) = 0

Combine like terms: -7z + 8z = 1z
(-28 + 1z + 2z2) = 0

Solving
-28 + 1z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(7 + -2z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve:

Simplifying
7 + -2z = 0

Solving
7 + -2z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2z = 0 + -7
-2z = 0 + -7

Combine like terms: 0 + -7 = -7
-2z = -7

Divide each side by '-2'.
z = 3.5

Simplifying
z = 3.5
Solution
z = {-4, 3.5}