12z^4-3z^2=0

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Solution for 12z^4-3z^2=0 equation:


Simplifying
12z4 + -3z2 = 0

Reorder the terms:
-3z2 + 12z4 = 0

Solving
-3z2 + 12z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z2'.
3z2(-1 + 4z2) = 0

Factor a difference between two squares.
3z2((1 + 2z)(-1 + 2z)) = 0

Ignore the factor 3.

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 '(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 '(-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

Solution

z = {0, -0.5, 0.5}

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