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

Solution for (4+z)(2z-3)=0 equation:

Simplifying
(4 + z)(2z + -3) = 0

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

Multiply (4 + z) * (-3 + 2z)
(4(-3 + 2z) + z(-3 + 2z)) = 0
((-3 * 4 + 2z * 4) + z(-3 + 2z)) = 0
((-12 + 8z) + z(-3 + 2z)) = 0
(-12 + 8z + (-3 * z + 2z * z)) = 0
(-12 + 8z + (-3z + 2z2)) = 0

Combine like terms: 8z + -3z = 5z
(-12 + 5z + 2z2) = 0

Solving
-12 + 5z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(3 + -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 '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-4, 1.5}