(3z-5)(z+1)=0

Solution for (3z-5)(z+1)=0 equation:

Simplifying
(3z + -5)(z + 1) = 0

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

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

Multiply (-5 + 3z) * (1 + z)
(-5(1 + z) + 3z * (1 + z)) = 0
((1 * -5 + z * -5) + 3z * (1 + z)) = 0
((-5 + -5z) + 3z * (1 + z)) = 0
(-5 + -5z + (1 * 3z + z * 3z)) = 0
(-5 + -5z + (3z + 3z2)) = 0

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

Solving
-5 + -2z + 3z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

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

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

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

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

Simplifying
z = -1
Subproblem 2
Set the factor '(5 + -3z)' equal to zero and attempt to solve:

Simplifying
5 + -3z = 0

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

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

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

Divide each side by '-3'.
z = 1.666666667

Simplifying
z = 1.666666667
Solution
z = {-1, 1.666666667}