(x^3+9x)-(4x^3-x)=0

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Solution for (x^3+9x)-(4x^3-x)=0 equation:


Simplifying
(x3 + 9x) + -1(4x3 + -1x) = 0

Reorder the terms:
(9x + x3) + -1(4x3 + -1x) = 0

Remove parenthesis around (9x + x3)
9x + x3 + -1(4x3 + -1x) = 0

Reorder the terms:
9x + x3 + -1(-1x + 4x3) = 0
9x + x3 + (-1x * -1 + 4x3 * -1) = 0
9x + x3 + (1x + -4x3) = 0

Reorder the terms:
9x + 1x + x3 + -4x3 = 0

Combine like terms: 9x + 1x = 10x
10x + x3 + -4x3 = 0

Combine like terms: x3 + -4x3 = -3x3
10x + -3x3 = 0

Solving
10x + -3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -3x2) = 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 '(10 + -3x2)' equal to zero and attempt to solve: Simplifying 10 + -3x2 = 0 Solving 10 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x2 = 0 + -10 -3x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -3x2 = -10 Divide each side by '-3'. x2 = 3.333333333 Simplifying x2 = 3.333333333 Take the square root of each side: x = {-1.825741858, 1.825741858}

Solution

x = {0, -1.825741858, 1.825741858}

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