4z^4-14z^3-30z^2=

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Solution for 4z^4-14z^3-30z^2= equation:


Simplifying
4z4 + -14z3 + -30z2 = 0

Reorder the terms:
-30z2 + -14z3 + 4z4 = 0

Solving
-30z2 + -14z3 + 4z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z2'.
2z2(-15 + -7z + 2z2) = 0

Factor a trinomial.
2z2((-3 + -2z)(5 + -1z)) = 0

Ignore the factor 2.

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 '(-3 + -2z)' equal to zero and attempt to solve: Simplifying -3 + -2z = 0 Solving -3 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2z = 0 + 3 -2z = 0 + 3 Combine like terms: 0 + 3 = 3 -2z = 3 Divide each side by '-2'. z = -1.5 Simplifying z = -1.5

Subproblem 3

Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5

Solution

z = {0, -1.5, 5}

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