(2z+7)(3-z)=0

Solution for (2z+7)(3-z)=0 equation:

Simplifying
(2z + 7)(3 + -1z) = 0

Reorder the terms:
(7 + 2z)(3 + -1z) = 0

Multiply (7 + 2z) * (3 + -1z)
(7(3 + -1z) + 2z * (3 + -1z)) = 0
((3 * 7 + -1z * 7) + 2z * (3 + -1z)) = 0
((21 + -7z) + 2z * (3 + -1z)) = 0
(21 + -7z + (3 * 2z + -1z * 2z)) = 0
(21 + -7z + (6z + -2z2)) = 0

Combine like terms: -7z + 6z = -1z
(21 + -1z + -2z2) = 0

Solving
21 + -1z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(7 + 2z) = 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 '(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 = {3, -3.5}