0=40x^3-24x

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Solution for 0=40x^3-24x equation:


Simplifying
0 = 40x3 + -24x

Reorder the terms:
0 = -24x + 40x3

Solving
0 = -24x + 40x3

Solving for variable 'x'.
Remove the zero:
24x + -40x3 = -24x + 40x3 + 24x + -40x3

Reorder the terms:
24x + -40x3 = -24x + 24x + 40x3 + -40x3

Combine like terms: -24x + 24x = 0
24x + -40x3 = 0 + 40x3 + -40x3
24x + -40x3 = 40x3 + -40x3

Combine like terms: 40x3 + -40x3 = 0
24x + -40x3 = 0

Factor out the Greatest Common Factor (GCF), '8x'.
8x(3 + -5x2) = 0

Ignore the factor 8.

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 + -5x2)' equal to zero and attempt to solve: Simplifying 3 + -5x2 = 0 Solving 3 + -5x2 = 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 + -5x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x2 = 0 + -3 -5x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5x2 = -3 Divide each side by '-5'. x2 = 0.6 Simplifying x2 = 0.6 Take the square root of each side: x = {-0.774596669, 0.774596669}

Solution

x = {0, -0.774596669, 0.774596669}

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