4z^4-20z^3-56z^2=0

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Solution for 4z^4-20z^3-56z^2=0 equation:


Simplifying
4z4 + -20z3 + -56z2 = 0

Reorder the terms:
-56z2 + -20z3 + 4z4 = 0

Solving
-56z2 + -20z3 + 4z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(-14 + -5z + z2) = 0

Factor a trinomial.
4z2((-2 + -1z)(7 + -1z)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}

Subproblem 2

Set the factor '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2

Subproblem 3

Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7

Solution

z = {0, -2, 7}

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