9x(x^2-2)=9x+2x^3

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Solution for 9x(x^2-2)=9x+2x^3 equation:


Simplifying
9x(x2 + -2) = 9x + 2x3

Reorder the terms:
9x(-2 + x2) = 9x + 2x3
(-2 * 9x + x2 * 9x) = 9x + 2x3
(-18x + 9x3) = 9x + 2x3

Solving
-18x + 9x3 = 9x + 2x3

Solving for variable 'x'.

Reorder the terms:
-18x + -9x + 9x3 + -2x3 = 9x + 2x3 + -9x + -2x3

Combine like terms: -18x + -9x = -27x
-27x + 9x3 + -2x3 = 9x + 2x3 + -9x + -2x3

Combine like terms: 9x3 + -2x3 = 7x3
-27x + 7x3 = 9x + 2x3 + -9x + -2x3

Reorder the terms:
-27x + 7x3 = 9x + -9x + 2x3 + -2x3

Combine like terms: 9x + -9x = 0
-27x + 7x3 = 0 + 2x3 + -2x3
-27x + 7x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-27x + 7x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27 + 7x2) = 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 '(-27 + 7x2)' equal to zero and attempt to solve: Simplifying -27 + 7x2 = 0 Solving -27 + 7x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 7x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 7x2 = 0 + 27 7x2 = 0 + 27 Combine like terms: 0 + 27 = 27 7x2 = 27 Divide each side by '7'. x2 = 3.857142857 Simplifying x2 = 3.857142857 Take the square root of each side: x = {-1.963961012, 1.963961012}

Solution

x = {0, -1.963961012, 1.963961012}

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