-[3z^2+6z-(2z^2-3z)]+[(6z^2-[5z-z^2])+5z^2]=0

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Solution for -[3z^2+6z-(2z^2-3z)]+[(6z^2-[5z-z^2])+5z^2]=0 equation: 


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

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

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

Combine like terms: 6z + 3z = 9z
-1[9z + 3z2 + -2z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0

Combine like terms: 3z2 + -2z2 = 1z2
-1[9z + 1z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0
[9z * -1 + 1z2 * -1] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0
[-9z + -1z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0
-9z + -1z2 + [(6z2 + [5z * -1 + -1z2 * -1]) + 5z2] = 0
-9z + -1z2 + [(6z2 + [-5z + 1z2]) + 5z2] = 0

Reorder the terms:
-9z + -1z2 + [(-5z + 6z2 + 1z2) + 5z2] = 0

Combine like terms: 6z2 + 1z2 = 7z2
-9z + -1z2 + [(-5z + 7z2) + 5z2] = 0

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

Combine like terms: 7z2 + 5z2 = 12z2
-9z + -1z2 + [-5z + 12z2] = 0

Remove brackets around [-5z + 12z2]
-9z + -1z2 + -5z + 12z2 = 0

Reorder the terms:
-9z + -5z + -1z2 + 12z2 = 0

Combine like terms: -9z + -5z = -14z
-14z + -1z2 + 12z2 = 0

Combine like terms: -1z2 + 12z2 = 11z2
-14z + 11z2 = 0

Solving
-14z + 11z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-14 + 11z) = 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 '(-14 + 11z)' equal to zero and attempt to solve:

Simplifying
-14 + 11z = 0

Solving
-14 + 11z = 0

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

Add '14' to each side of the equation.
-14 + 14 + 11z = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 11z = 0 + 14
11z = 0 + 14

Combine like terms: 0 + 14 = 14
11z = 14

Divide each side by '11'.
z = 1.272727273

Simplifying
z = 1.272727273
Solution
z = {0, 1.272727273}

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