-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 = -0.067816434
z = -0.067816434

Simplifying
z = -0.067816434

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 = -3.932183566
z = -3.932183566

Simplifying
z = -3.932183566

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