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

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

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

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

Multiply (5 + z) * (-3 + 2z)
(5(-3 + 2z) + z(-3 + 2z)) = 0
((-3 * 5 + 2z * 5) + z(-3 + 2z)) = 0
((-15 + 10z) + z(-3 + 2z)) = 0
(-15 + 10z + (-3 * z + 2z * z)) = 0
(-15 + 10z + (-3z + 2z2)) = 0

Combine like terms: 10z + -3z = 7z
(-15 + 7z + 2z2) = 0

Solving
-15 + 7z + 2z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
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 = {-5, 1.5}