12z^3=10z^2+8z

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Solution for 12z^3=10z^2+8z equation:


Simplifying
12z3 = 10z2 + 8z

Reorder the terms:
12z3 = 8z + 10z2

Solving
12z3 = 8z + 10z2

Solving for variable 'z'.

Reorder the terms:
-8z + -10z2 + 12z3 = 8z + 10z2 + -8z + -10z2

Reorder the terms:
-8z + -10z2 + 12z3 = 8z + -8z + 10z2 + -10z2

Combine like terms: 8z + -8z = 0
-8z + -10z2 + 12z3 = 0 + 10z2 + -10z2
-8z + -10z2 + 12z3 = 10z2 + -10z2

Combine like terms: 10z2 + -10z2 = 0
-8z + -10z2 + 12z3 = 0

Factor out the Greatest Common Factor (GCF), '2z'.
2z(-4 + -5z + 6z2) = 0

Factor a trinomial.
2z((-1 + -2z)(4 + -3z)) = 0

Ignore the factor 2.

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 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 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 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5

Subproblem 3

Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333

Solution

z = {0, -0.5, 1.333333333}

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