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

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

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

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

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

Multiply (-1 + 8z) * (3 + z)
(-1(3 + z) + 8z * (3 + z)) = 0
((3 * -1 + z * -1) + 8z * (3 + z)) = 0
((-3 + -1z) + 8z * (3 + z)) = 0
(-3 + -1z + (3 * 8z + z * 8z)) = 0
(-3 + -1z + (24z + 8z2)) = 0

Combine like terms: -1z + 24z = 23z
(-3 + 23z + 8z2) = 0

Solving
-3 + 23z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(1 + -8z) = 0

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

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 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 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(1 + -8z)' equal to zero and attempt to solve:

Simplifying
1 + -8z = 0

Solving
1 + -8z = 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 + -8z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8z = 0 + -1
-8z = 0 + -1

Combine like terms: 0 + -1 = -1
-8z = -1

Divide each side by '-8'.
z = 0.125

Simplifying
z = 0.125
Solution
z = {-3, 0.125}