z^7+2(z^4)+4z=0

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Solution for z^7+2(z^4)+4z=0 equation:


Simplifying
z7 + 2(z4) + 4z = 0

Reorder the terms:
4z + 2z4 + z7 = 0

Solving
4z + 2z4 + z7 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + 2z3 + z6) = 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 + 2z3 + z6)' equal to zero and attempt to solve: Simplifying 4 + 2z3 + z6 = 0 Solving 4 + 2z3 + z6 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2z3 + -4 + z6 = 0 + -4 Reorder the terms: 4 + -4 + 2z3 + z6 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2z3 + z6 = 0 + -4 2z3 + z6 = 0 + -4 Combine like terms: 0 + -4 = -4 2z3 + z6 = -4 The z term is 2z3. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2z3 + 1 + z6 = -4 + 1 Reorder the terms: 1 + 2z3 + z6 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + 2z3 + z6 = -3 Factor a perfect square on the left side: (z3 + 1)(z3 + 1) = -3 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

z = {0}

 

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