(3z-8)(1+z)=0

Solution for (3z-8)(1+z)=0 equation:

Simplifying
(3z + -8)(1 + z) = 0

Reorder the terms:
(-8 + 3z)(1 + z) = 0

Multiply (-8 + 3z) * (1 + z)
(-8(1 + z) + 3z * (1 + z)) = 0
((1 * -8 + z * -8) + 3z * (1 + z)) = 0
((-8 + -8z) + 3z * (1 + z)) = 0
(-8 + -8z + (1 * 3z + z * 3z)) = 0
(-8 + -8z + (3z + 3z2)) = 0

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

Solving
-8 + -5z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z)(8 + -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 '(8 + -3z)' equal to zero and attempt to solve:

Simplifying
8 + -3z = 0

Solving
8 + -3z = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3z = 0 + -8
-3z = 0 + -8

Combine like terms: 0 + -8 = -8
-3z = -8

Divide each side by '-3'.
z = 2.666666667

Simplifying
z = 2.666666667
Solution
z = {-1, 2.666666667}