x^3+9x=6x^2

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Solution for x^3+9x=6x^2 equation:


Simplifying
x3 + 9x = 6x2

Reorder the terms:
9x + x3 = 6x2

Solving
9x + x3 = 6x2

Solving for variable 'x'.

Reorder the terms:
9x + -6x2 + x3 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
9x + -6x2 + x3 = 0

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

Factor a trinomial.
x((3 + -1x)(3 + -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 x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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

Subproblem 3

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

Solution

x = {0, 3, 3}

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