x^6+4ax^3+4a^2=0

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Solution for x^6+4ax^3+4a^2=0 equation:


Simplifying
x6 + 4ax3 + 4a2 = 0

Reorder the terms:
4ax3 + 4a2 + x6 = 0

Solving
4ax3 + 4a2 + x6 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + x3)(2a + x3) = 0

Subproblem 1

Set the factor '(2a + x3)' equal to zero and attempt to solve: Simplifying 2a + x3 = 0 Solving 2a + x3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x3' to each side of the equation. 2a + x3 + -1x3 = 0 + -1x3 Combine like terms: x3 + -1x3 = 0 2a + 0 = 0 + -1x3 2a = 0 + -1x3 Remove the zero: 2a = -1x3 Divide each side by '2'. a = -0.5x3 Simplifying a = -0.5x3

Subproblem 2

Set the factor '(2a + x3)' equal to zero and attempt to solve: Simplifying 2a + x3 = 0 Solving 2a + x3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x3' to each side of the equation. 2a + x3 + -1x3 = 0 + -1x3 Combine like terms: x3 + -1x3 = 0 2a + 0 = 0 + -1x3 2a = 0 + -1x3 Remove the zero: 2a = -1x3 Divide each side by '2'. a = -0.5x3 Simplifying a = -0.5x3

Solution

a = {-0.5x3, -0.5x3}

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