3z^3=4z^2+7z

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Solution for 3z^3=4z^2+7z equation:


Simplifying
3z3 = 4z2 + 7z

Reorder the terms:
3z3 = 7z + 4z2

Solving
3z3 = 7z + 4z2

Solving for variable 'z'.

Reorder the terms:
-7z + -4z2 + 3z3 = 7z + 4z2 + -7z + -4z2

Reorder the terms:
-7z + -4z2 + 3z3 = 7z + -7z + 4z2 + -4z2

Combine like terms: 7z + -7z = 0
-7z + -4z2 + 3z3 = 0 + 4z2 + -4z2
-7z + -4z2 + 3z3 = 4z2 + -4z2

Combine like terms: 4z2 + -4z2 = 0
-7z + -4z2 + 3z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-7 + -4z + 3z2) = 0

Factor a trinomial.
z((-1 + -1z)(7 + -3z)) = 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 '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1

Subproblem 3

Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 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 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333

Solution

z = {0, -1, 2.333333333}

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