0=x^3-6ax^2+9a^2*x

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Solution for 0=x^3-6ax^2+9a^2*x equation:


Simplifying
0 = x3 + -6ax2 + 9a2 * x

Multiply a2 * x
0 = x3 + -6ax2 + 9a2x

Reorder the terms:
0 = -6ax2 + 9a2x + x3

Solving
0 = -6ax2 + 9a2x + x3

Solving for variable 'a'.
Remove the zero:
6ax2 + -9a2x + -1x3 = -6ax2 + 9a2x + x3 + 6ax2 + -9a2x + -1x3

Reorder the terms:
6ax2 + -9a2x + -1x3 = -6ax2 + 6ax2 + 9a2x + -9a2x + x3 + -1x3

Combine like terms: -6ax2 + 6ax2 = 0
6ax2 + -9a2x + -1x3 = 0 + 9a2x + -9a2x + x3 + -1x3
6ax2 + -9a2x + -1x3 = 9a2x + -9a2x + x3 + -1x3

Combine like terms: 9a2x + -9a2x = 0
6ax2 + -9a2x + -1x3 = 0 + x3 + -1x3
6ax2 + -9a2x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
6ax2 + -9a2x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6ax + -9a2 + -1x2) = 0

Factor a trinomial.
x((-3a + x)(3a + -1x)) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-3a + x)' equal to zero and attempt to solve: Simplifying -3a + x = 0 Solving -3a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. -3a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 -3a + 0 = 0 + -1x -3a = 0 + -1x Remove the zero: -3a = -1x Divide each side by '-3'. a = 0.3333333333x Simplifying a = 0.3333333333x

Subproblem 3

Set the factor '(3a + -1x)' equal to zero and attempt to solve: Simplifying 3a + -1x = 0 Solving 3a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. 3a + -1x + x = 0 + x Combine like terms: -1x + x = 0 3a + 0 = 0 + x 3a = 0 + x Remove the zero: 3a = x Divide each side by '3'. a = 0.3333333333x Simplifying a = 0.3333333333x

Solution

a = {0.3333333333x, 0.3333333333x}

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