-2x^2=24x-x^3

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Solution for -2x^2=24x-x^3 equation:


Simplifying
-2x2 = 24x + -1x3

Solving
-2x2 = 24x + -1x3

Solving for variable 'x'.

Reorder the terms:
-24x + -2x2 + x3 = 24x + -1x3 + -24x + x3

Reorder the terms:
-24x + -2x2 + x3 = 24x + -24x + -1x3 + x3

Combine like terms: 24x + -24x = 0
-24x + -2x2 + x3 = 0 + -1x3 + x3
-24x + -2x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-24x + -2x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + -2x + x2) = 0

Factor a trinomial.
x((-4 + -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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

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, -4, 6}

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