2z^3=7z^2+9z

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Solution for 2z^3=7z^2+9z equation:


Simplifying
2z3 = 7z2 + 9z

Reorder the terms:
2z3 = 9z + 7z2

Solving
2z3 = 9z + 7z2

Solving for variable 'z'.

Reorder the terms:
-9z + -7z2 + 2z3 = 9z + 7z2 + -9z + -7z2

Reorder the terms:
-9z + -7z2 + 2z3 = 9z + -9z + 7z2 + -7z2

Combine like terms: 9z + -9z = 0
-9z + -7z2 + 2z3 = 0 + 7z2 + -7z2
-9z + -7z2 + 2z3 = 7z2 + -7z2

Combine like terms: 7z2 + -7z2 = 0
-9z + -7z2 + 2z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-9 + -7z + 2z2) = 0

Factor a trinomial.
z((-1 + -1z)(9 + -2z)) = 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 '(9 + -2z)' equal to zero and attempt to solve: Simplifying 9 + -2z = 0 Solving 9 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2z = 0 + -9 -2z = 0 + -9 Combine like terms: 0 + -9 = -9 -2z = -9 Divide each side by '-2'. z = 4.5 Simplifying z = 4.5

Solution

z = {0, -1, 4.5}

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