[3z^2+5z-(2z^2-4z)]+[(7z^2-[5z-z^2])+2z^2]=

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Solution for [3z^2+5z-(2z^2-4z)]+[(7z^2-[5z-z^2])+2z^2]= equation:


Simplifying
[3z2 + 5z + -1(2z2 + -4z)] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0

Reorder the terms:
[3z2 + 5z + -1(-4z + 2z2)] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0
[3z2 + 5z + (-4z * -1 + 2z2 * -1)] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0
[3z2 + 5z + (4z + -2z2)] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0

Reorder the terms:
[5z + 4z + 3z2 + -2z2] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0

Combine like terms: 5z + 4z = 9z
[9z + 3z2 + -2z2] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0

Combine like terms: 3z2 + -2z2 = 1z2
[9z + 1z2] + [(7z2 + -1[5z + -1z2]) + 2z2] = 0

Remove brackets around [9z + 1z2]
9z + 1z2 + [(7z2 + -1[5z + -1z2]) + 2z2] = 0
9z + 1z2 + [(7z2 + [5z * -1 + -1z2 * -1]) + 2z2] = 0
9z + 1z2 + [(7z2 + [-5z + 1z2]) + 2z2] = 0

Reorder the terms:
9z + 1z2 + [(-5z + 7z2 + 1z2) + 2z2] = 0

Combine like terms: 7z2 + 1z2 = 8z2
9z + 1z2 + [(-5z + 8z2) + 2z2] = 0

Remove parenthesis around (-5z + 8z2)
9z + 1z2 + [-5z + 8z2 + 2z2] = 0

Combine like terms: 8z2 + 2z2 = 10z2
9z + 1z2 + [-5z + 10z2] = 0

Remove brackets around [-5z + 10z2]
9z + 1z2 + -5z + 10z2 = 0

Reorder the terms:
9z + -5z + 1z2 + 10z2 = 0

Combine like terms: 9z + -5z = 4z
4z + 1z2 + 10z2 = 0

Combine like terms: 1z2 + 10z2 = 11z2
4z + 11z2 = 0

Solving
4z + 11z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + 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 '(4 + 11z)' equal to zero and attempt to solve: Simplifying 4 + 11z = 0 Solving 4 + 11z = 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 + 11z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 11z = 0 + -4 11z = 0 + -4 Combine like terms: 0 + -4 = -4 11z = -4 Divide each side by '11'. z = -0.3636363636 Simplifying z = -0.3636363636

Solution

z = {0, -0.3636363636}

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