-[3z^2+7z-(2z^2-5z)]+[(10z^2-[5z-z^2])+3z^2]=

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Solution for -[3z^2+7z-(2z^2-5z)]+[(10z^2-[5z-z^2])+3z^2]= equation:


Simplifying
-1[3z2 + 7z + -1(2z2 + -5z)] + [(10z2 + -1[5z + -1z2]) + 3z2] = 0

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

Reorder the terms:
-1[7z + 5z + 3z2 + -2z2] + [(10z2 + -1[5z + -1z2]) + 3z2] = 0

Combine like terms: 7z + 5z = 12z
-1[12z + 3z2 + -2z2] + [(10z2 + -1[5z + -1z2]) + 3z2] = 0

Combine like terms: 3z2 + -2z2 = 1z2
-1[12z + 1z2] + [(10z2 + -1[5z + -1z2]) + 3z2] = 0
[12z * -1 + 1z2 * -1] + [(10z2 + -1[5z + -1z2]) + 3z2] = 0
[-12z + -1z2] + [(10z2 + -1[5z + -1z2]) + 3z2] = 0
-12z + -1z2 + [(10z2 + [5z * -1 + -1z2 * -1]) + 3z2] = 0
-12z + -1z2 + [(10z2 + [-5z + 1z2]) + 3z2] = 0

Reorder the terms:
-12z + -1z2 + [(-5z + 10z2 + 1z2) + 3z2] = 0

Combine like terms: 10z2 + 1z2 = 11z2
-12z + -1z2 + [(-5z + 11z2) + 3z2] = 0

Remove parenthesis around (-5z + 11z2)
-12z + -1z2 + [-5z + 11z2 + 3z2] = 0

Combine like terms: 11z2 + 3z2 = 14z2
-12z + -1z2 + [-5z + 14z2] = 0

Remove brackets around [-5z + 14z2]
-12z + -1z2 + -5z + 14z2 = 0

Reorder the terms:
-12z + -5z + -1z2 + 14z2 = 0

Combine like terms: -12z + -5z = -17z
-17z + -1z2 + 14z2 = 0

Combine like terms: -1z2 + 14z2 = 13z2
-17z + 13z2 = 0

Solving
-17z + 13z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-17 + 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 '(-17 + 13z)' equal to zero and attempt to solve: Simplifying -17 + 13z = 0 Solving -17 + 13z = 0 Move all terms containing z to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 13z = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 13z = 0 + 17 13z = 0 + 17 Combine like terms: 0 + 17 = 17 13z = 17 Divide each side by '13'. z = 1.307692308 Simplifying z = 1.307692308

Solution

z = {0, 1.307692308}

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