4z^3+9z=12z^2

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Solution for 4z^3+9z=12z^2 equation:


Simplifying
4z3 + 9z = 12z2

Reorder the terms:
9z + 4z3 = 12z2

Solving
9z + 4z3 = 12z2

Solving for variable 'z'.

Reorder the terms:
9z + -12z2 + 4z3 = 12z2 + -12z2

Combine like terms: 12z2 + -12z2 = 0
9z + -12z2 + 4z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(9 + -12z + 4z2) = 0

Factor a trinomial.
z((3 + -2z)(3 + -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 '(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 '(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

Solution

z = {0, 1.5, 1.5}

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