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

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

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

Reorder the terms:
(-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.
(-3 + -2z)(5 + -1z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
z = {-1.5, 5}