x^3=9x^2-18x

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Solution for x^3=9x^2-18x equation:


Simplifying
x3 = 9x2 + -18x

Reorder the terms:
x3 = -18x + 9x2

Solving
x3 = -18x + 9x2

Solving for variable 'x'.

Reorder the terms:
18x + -9x2 + x3 = -18x + 9x2 + 18x + -9x2

Reorder the terms:
18x + -9x2 + x3 = -18x + 18x + 9x2 + -9x2

Combine like terms: -18x + 18x = 0
18x + -9x2 + x3 = 0 + 9x2 + -9x2
18x + -9x2 + x3 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
18x + -9x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(18 + -9x + x2) = 0

Factor a trinomial.
x((3 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {0, 3, 6}

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