(z+6)(5z-8)=0

Solution for (z+6)(5z-8)=0 equation:

Simplifying
(z + 6)(5z + -8) = 0

Reorder the terms:
(6 + z)(5z + -8) = 0

Reorder the terms:
(6 + z)(-8 + 5z) = 0

Multiply (6 + z) * (-8 + 5z)
(6(-8 + 5z) + z(-8 + 5z)) = 0
((-8 * 6 + 5z * 6) + z(-8 + 5z)) = 0
((-48 + 30z) + z(-8 + 5z)) = 0
(-48 + 30z + (-8 * z + 5z * z)) = 0
(-48 + 30z + (-8z + 5z2)) = 0

Combine like terms: 30z + -8z = 22z
(-48 + 22z + 5z2) = 0

Solving
-48 + 22z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(8 + -5z) = 0

Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(8 + -5z)' equal to zero and attempt to solve:

Simplifying
8 + -5z = 0

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

Combine like terms: 8 + -8 = 0
0 + -5z = 0 + -8
-5z = 0 + -8

Combine like terms: 0 + -8 = -8
-5z = -8

Divide each side by '-5'.
z = 1.6

Simplifying
z = 1.6
Solution
z = {-6, 1.6}