-[7z(14z+10)]=10+(6z+1)

Solution for -[7z(14z+10)]=10+(6z+1) equation:

Simplifying
-1[7z(14z + 10)] = 10 + (6z + 1)

Reorder the terms:
-1[7z(10 + 14z)] = 10 + (6z + 1)
-1[(10 * 7z + 14z * 7z)] = 10 + (6z + 1)
-1[(70z + 98z2)] = 10 + (6z + 1)
[70z * -1 + 98z2 * -1] = 10 + (6z + 1)
[-70z + -98z2] = 10 + (6z + 1)

Reorder the terms:
-70z + -98z2 = 10 + (1 + 6z)

Remove parenthesis around (1 + 6z)
-70z + -98z2 = 10 + 1 + 6z

Combine like terms: 10 + 1 = 11
-70z + -98z2 = 11 + 6z

Solving
-70z + -98z2 = 11 + 6z

Solving for variable 'z'.

Reorder the terms:
-11 + -70z + -6z + -98z2 = 11 + 6z + -11 + -6z

Combine like terms: -70z + -6z = -76z
-11 + -76z + -98z2 = 11 + 6z + -11 + -6z

Reorder the terms:
-11 + -76z + -98z2 = 11 + -11 + 6z + -6z

Combine like terms: 11 + -11 = 0
-11 + -76z + -98z2 = 0 + 6z + -6z
-11 + -76z + -98z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-11 + -76z + -98z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 76z + 98z2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + 76z + 98z2)' equal to zero and attempt to solve:

Simplifying
11 + 76z + 98z2 = 0

Solving
11 + 76z + 98z2 = 0

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

Divide each side by '98'.
0.112244898 + 0.7755102041z + z2 = 0

Move the constant term to the right:

Add '-0.112244898' to each side of the equation.
0.112244898 + 0.7755102041z + -0.112244898 + z2 = 0 + -0.112244898

Reorder the terms:
0.112244898 + -0.112244898 + 0.7755102041z + z2 = 0 + -0.112244898

Combine like terms: 0.112244898 + -0.112244898 = 0.000000000
0.000000000 + 0.7755102041z + z2 = 0 + -0.112244898
0.7755102041z + z2 = 0 + -0.112244898

Combine like terms: 0 + -0.112244898 = -0.112244898
0.7755102041z + z2 = -0.112244898

The z term is 0.7755102041z.  Take half its coefficient (0.3877551021).
Square it (0.1503540192) and add it to both sides.

Add '0.1503540192' to each side of the equation.
0.7755102041z + 0.1503540192 + z2 = -0.112244898 + 0.1503540192

Reorder the terms:
0.1503540192 + 0.7755102041z + z2 = -0.112244898 + 0.1503540192

Combine like terms: -0.112244898 + 0.1503540192 = 0.0381091212
0.1503540192 + 0.7755102041z + z2 = 0.0381091212

Factor a perfect square on the left side:
(z + 0.3877551021)(z + 0.3877551021) = 0.0381091212

Calculate the square root of the right side: 0.195215576

Break this problem into two subproblems by setting 
(z + 0.3877551021) equal to 0.195215576 and -0.195215576.

Subproblem 1
z + 0.3877551021 = 0.195215576

Simplifying
z + 0.3877551021 = 0.195215576

Reorder the terms:
0.3877551021 + z = 0.195215576

Solving
0.3877551021 + z = 0.195215576

Solving for variable 'z'.

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

Add '-0.3877551021' to each side of the equation.
0.3877551021 + -0.3877551021 + z = 0.195215576 + -0.3877551021

Combine like terms: 0.3877551021 + -0.3877551021 = 0.0000000000
0.0000000000 + z = 0.195215576 + -0.3877551021
z = 0.195215576 + -0.3877551021

Combine like terms: 0.195215576 + -0.3877551021 = -0.1925395261
z = -0.1925395261

Simplifying
z = -0.1925395261

Subproblem 2
z + 0.3877551021 = -0.195215576

Simplifying
z + 0.3877551021 = -0.195215576

Reorder the terms:
0.3877551021 + z = -0.195215576

Solving
0.3877551021 + z = -0.195215576

Solving for variable 'z'.

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

Add '-0.3877551021' to each side of the equation.
0.3877551021 + -0.3877551021 + z = -0.195215576 + -0.3877551021

Combine like terms: 0.3877551021 + -0.3877551021 = 0.0000000000
0.0000000000 + z = -0.195215576 + -0.3877551021
z = -0.195215576 + -0.3877551021

Combine like terms: -0.195215576 + -0.3877551021 = -0.5829706781
z = -0.5829706781

Simplifying
z = -0.5829706781

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.1925395261, -0.5829706781}
Solution
z = {-0.1925395261, -0.5829706781}