-[3z^2+6z-(2z^2-5z)]+[(10z^2-[5z-z^2])+4z^2]=

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Solution for -[3z^2+6z-(2z^2-5z)]+[(10z^2-[5z-z^2])+4z^2]= equation: 


Simplifying
-1[3z2 + 6z + -1(2z2 + -5z)] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0

Reorder the terms:
-1[3z2 + 6z + -1(-5z + 2z2)] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0
-1[3z2 + 6z + (-5z * -1 + 2z2 * -1)] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0
-1[3z2 + 6z + (5z + -2z2)] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0

Reorder the terms:
-1[6z + 5z + 3z2 + -2z2] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0

Combine like terms: 6z + 5z = 11z
-1[11z + 3z2 + -2z2] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0

Combine like terms: 3z2 + -2z2 = 1z2
-1[11z + 1z2] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0
[11z * -1 + 1z2 * -1] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0
[-11z + -1z2] + [(10z2 + -1[5z + -1z2]) + 4z2] = 0
-11z + -1z2 + [(10z2 + [5z * -1 + -1z2 * -1]) + 4z2] = 0
-11z + -1z2 + [(10z2 + [-5z + 1z2]) + 4z2] = 0

Reorder the terms:
-11z + -1z2 + [(-5z + 10z2 + 1z2) + 4z2] = 0

Combine like terms: 10z2 + 1z2 = 11z2
-11z + -1z2 + [(-5z + 11z2) + 4z2] = 0

Remove parenthesis around (-5z + 11z2)
-11z + -1z2 + [-5z + 11z2 + 4z2] = 0

Combine like terms: 11z2 + 4z2 = 15z2
-11z + -1z2 + [-5z + 15z2] = 0

Remove brackets around [-5z + 15z2]
-11z + -1z2 + -5z + 15z2 = 0

Reorder the terms:
-11z + -5z + -1z2 + 15z2 = 0

Combine like terms: -11z + -5z = -16z
-16z + -1z2 + 15z2 = 0

Combine like terms: -1z2 + 15z2 = 14z2
-16z + 14z2 = 0

Solving
-16z + 14z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(-8 + 7z) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

Subproblem 2
Set the factor '(-8 + 7z)' equal to zero and attempt to solve:

Simplifying
-8 + 7z = 0

Solving
-8 + 7z = 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 + 7z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 7z = 0 + 8
7z = 0 + 8

Combine like terms: 0 + 8 = 8
7z = 8

Divide each side by '7'.
z = 1.142857143

Simplifying
z = 1.142857143
Solution
z = {0, 1.142857143}

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