-3(2z-8)10z=16

Solution for -3(2z-8)10z=16 equation:

Simplifying
-3(2z + -8) * 10z = 16

Reorder the terms:
-3(-8 + 2z) * 10z = 16

Reorder the terms for easier multiplication:
-3 * 10z(-8 + 2z) = 16

Multiply -3 * 10
-30z(-8 + 2z) = 16
(-8 * -30z + 2z * -30z) = 16
(240z + -60z2) = 16

Solving
240z + -60z2 = 16

Solving for variable 'z'.

Reorder the terms:
-16 + 240z + -60z2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 240z + -60z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 60z + -15z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + 60z + -15z2)' equal to zero and attempt to solve:

Simplifying
-4 + 60z + -15z2 = 0

Solving
-4 + 60z + -15z2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.2666666667 + -4z + z2 = 0

Move the constant term to the right:

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -4z + -0.2666666667 + z2 = 0 + -0.2666666667

Reorder the terms:
0.2666666667 + -0.2666666667 + -4z + z2 = 0 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + -4z + z2 = 0 + -0.2666666667
-4z + z2 = 0 + -0.2666666667

Combine like terms: 0 + -0.2666666667 = -0.2666666667
-4z + z2 = -0.2666666667

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = -0.2666666667 + 4

Reorder the terms:
4 + -4z + z2 = -0.2666666667 + 4

Combine like terms: -0.2666666667 + 4 = 3.7333333333
4 + -4z + z2 = 3.7333333333

Factor a perfect square on the left side:
(z + -2)(z + -2) = 3.7333333333

Calculate the square root of the right side: 1.932183566

Break this problem into two subproblems by setting 
(z + -2) equal to 1.932183566 and -1.932183566.

Subproblem 1
z + -2 = 1.932183566

Simplifying
z + -2 = 1.932183566

Reorder the terms:
-2 + z = 1.932183566

Solving
-2 + z = 1.932183566

Solving for variable 'z'.

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

Add '2' to each side of the equation.
-2 + 2 + z = 1.932183566 + 2

Combine like terms: -2 + 2 = 0
0 + z = 1.932183566 + 2
z = 1.932183566 + 2

Combine like terms: 1.932183566 + 2 = 3.932183566
z = 3.932183566

Simplifying
z = 3.932183566

Subproblem 2
z + -2 = -1.932183566

Simplifying
z + -2 = -1.932183566

Reorder the terms:
-2 + z = -1.932183566

Solving
-2 + z = -1.932183566

Solving for variable 'z'.

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

Add '2' to each side of the equation.
-2 + 2 + z = -1.932183566 + 2

Combine like terms: -2 + 2 = 0
0 + z = -1.932183566 + 2
z = -1.932183566 + 2

Combine like terms: -1.932183566 + 2 = 0.067816434
z = 0.067816434

Simplifying
z = 0.067816434

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.932183566, 0.067816434}
Solution
z = {3.932183566, 0.067816434}