-[3z^2+2z-(2z^2-5z)]+[(8z^2-[5z-z^2])+5z^2]=0

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Solution for -[3z^2+2z-(2z^2-5z)]+[(8z^2-[5z-z^2])+5z^2]=0 equation: 


Simplifying
-1[3z2 + 2z + -1(2z2 + -5z)] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0

Reorder the terms:
-1[3z2 + 2z + -1(-5z + 2z2)] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0
-1[3z2 + 2z + (-5z * -1 + 2z2 * -1)] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0
-1[3z2 + 2z + (5z + -2z2)] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0

Reorder the terms:
-1[2z + 5z + 3z2 + -2z2] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0

Combine like terms: 2z + 5z = 7z
-1[7z + 3z2 + -2z2] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0

Combine like terms: 3z2 + -2z2 = 1z2
-1[7z + 1z2] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0
[7z * -1 + 1z2 * -1] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0
[-7z + -1z2] + [(8z2 + -1[5z + -1z2]) + 5z2] = 0
-7z + -1z2 + [(8z2 + [5z * -1 + -1z2 * -1]) + 5z2] = 0
-7z + -1z2 + [(8z2 + [-5z + 1z2]) + 5z2] = 0

Reorder the terms:
-7z + -1z2 + [(-5z + 8z2 + 1z2) + 5z2] = 0

Combine like terms: 8z2 + 1z2 = 9z2
-7z + -1z2 + [(-5z + 9z2) + 5z2] = 0

Remove parenthesis around (-5z + 9z2)
-7z + -1z2 + [-5z + 9z2 + 5z2] = 0

Combine like terms: 9z2 + 5z2 = 14z2
-7z + -1z2 + [-5z + 14z2] = 0

Remove brackets around [-5z + 14z2]
-7z + -1z2 + -5z + 14z2 = 0

Reorder the terms:
-7z + -5z + -1z2 + 14z2 = 0

Combine like terms: -7z + -5z = -12z
-12z + -1z2 + 14z2 = 0

Combine like terms: -1z2 + 14z2 = 13z2
-12z + 13z2 = 0

Solving
-12z + 13z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-12 + 13z) = 0


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 '(-12 + 13z)' equal to zero and attempt to solve:

Simplifying
-12 + 13z = 0

Solving
-12 + 13z = 0

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

Add '12' to each side of the equation.
-12 + 12 + 13z = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 13z = 0 + 12
13z = 0 + 12

Combine like terms: 0 + 12 = 12
13z = 12

Divide each side by '13'.
z = 0.9230769231

Simplifying
z = 0.9230769231
Solution
z = {0, 0.9230769231}

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