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

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


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

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

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

Combine like terms: 4z + 3z = 7z
-1[7z + 3z2 + -2z2] + [(10z2 + -1[5z + -1z2]) + 5z2] = 0

Combine like terms: 3z2 + -2z2 = 1z2
-1[7z + 1z2] + [(10z2 + -1[5z + -1z2]) + 5z2] = 0
[7z * -1 + 1z2 * -1] + [(10z2 + -1[5z + -1z2]) + 5z2] = 0
[-7z + -1z2] + [(10z2 + -1[5z + -1z2]) + 5z2] = 0
-7z + -1z2 + [(10z2 + [5z * -1 + -1z2 * -1]) + 5z2] = 0
-7z + -1z2 + [(10z2 + [-5z + 1z2]) + 5z2] = 0

Reorder the terms:
-7z + -1z2 + [(-5z + 10z2 + 1z2) + 5z2] = 0

Combine like terms: 10z2 + 1z2 = 11z2
-7z + -1z2 + [(-5z + 11z2) + 5z2] = 0

Remove parenthesis around (-5z + 11z2)
-7z + -1z2 + [-5z + 11z2 + 5z2] = 0

Combine like terms: 11z2 + 5z2 = 16z2
-7z + -1z2 + [-5z + 16z2] = 0

Remove brackets around [-5z + 16z2]
-7z + -1z2 + -5z + 16z2 = 0

Reorder the terms:
-7z + -5z + -1z2 + 16z2 = 0

Combine like terms: -7z + -5z = -12z
-12z + -1z2 + 16z2 = 0

Combine like terms: -1z2 + 16z2 = 15z2
-12z + 15z2 = 0

Solving
-12z + 15z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-4 + 5z) = 0

Ignore the factor 3.

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 '(-4 + 5z)' equal to zero and attempt to solve:

Simplifying
-4 + 5z = 0

Solving
-4 + 5z = 0

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

Add '4' to each side of the equation.
-4 + 4 + 5z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5z = 0 + 4
5z = 0 + 4

Combine like terms: 0 + 4 = 4
5z = 4

Divide each side by '5'.
z = 0.8

Simplifying
z = 0.8
Solution
z = {0, 0.8}

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