x^3=18x-7x^2

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Solution for x^3=18x-7x^2 equation:


Simplifying
x3 = 18x + -7x2

Solving
x3 = 18x + -7x2

Solving for variable 'x'.

Reorder the terms:
-18x + 7x2 + x3 = 18x + -7x2 + -18x + 7x2

Reorder the terms:
-18x + 7x2 + x3 = 18x + -18x + -7x2 + 7x2

Combine like terms: 18x + -18x = 0
-18x + 7x2 + x3 = 0 + -7x2 + 7x2
-18x + 7x2 + x3 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-18x + 7x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + 7x + x2) = 0

Factor a trinomial.
x((-9 + -1x)(2 + -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 '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 3

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

Solution

x = {0, -9, 2}

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