(5z-3)(2+z)=0

Solution for (5z-3)(2+z)=0 equation:

Simplifying
(5z + -3)(2 + z) = 0

Reorder the terms:
(-3 + 5z)(2 + z) = 0

Multiply (-3 + 5z) * (2 + z)
(-3(2 + z) + 5z * (2 + z)) = 0
((2 * -3 + z * -3) + 5z * (2 + z)) = 0
((-6 + -3z) + 5z * (2 + z)) = 0
(-6 + -3z + (2 * 5z + z * 5z)) = 0
(-6 + -3z + (10z + 5z2)) = 0

Combine like terms: -3z + 10z = 7z
(-6 + 7z + 5z2) = 0

Solving
-6 + 7z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z)(3 + -5z) = 0

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(3 + -5z)' equal to zero and attempt to solve:

Simplifying
3 + -5z = 0

Solving
3 + -5z = 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 + -5z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5z = 0 + -3
-5z = 0 + -3

Combine like terms: 0 + -3 = -3
-5z = -3

Divide each side by '-5'.
z = 0.6

Simplifying
z = 0.6
Solution
z = {-2, 0.6}