2x^3=5x^2+12x+0

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Solution for 2x^3=5x^2+12x+0 equation:


Simplifying
2x3 = 5x2 + 12x + 0

Reorder the terms:
2x3 = 0 + 12x + 5x2
Remove the zero:
2x3 = 12x + 5x2

Solving
2x3 = 12x + 5x2

Solving for variable 'x'.

Reorder the terms:
-12x + -5x2 + 2x3 = 12x + 5x2 + -12x + -5x2

Reorder the terms:
-12x + -5x2 + 2x3 = 12x + -12x + 5x2 + -5x2

Combine like terms: 12x + -12x = 0
-12x + -5x2 + 2x3 = 0 + 5x2 + -5x2
-12x + -5x2 + 2x3 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-12x + -5x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12 + -5x + 2x2) = 0

Factor a trinomial.
x((-3 + -2x)(4 + -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 '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 3

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

Solution

x = {0, -1.5, 4}

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