5x^2=6x+x^3

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Solution for 5x^2=6x+x^3 equation:


Simplifying
5x2 = 6x + x3

Solving
5x2 = 6x + x3

Solving for variable 'x'.

Reorder the terms:
-6x + 5x2 + -1x3 = 6x + x3 + -6x + -1x3

Reorder the terms:
-6x + 5x2 + -1x3 = 6x + -6x + x3 + -1x3

Combine like terms: 6x + -6x = 0
-6x + 5x2 + -1x3 = 0 + x3 + -1x3
-6x + 5x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-6x + 5x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 5x + -1x2) = 0

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

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0, 3, 2}

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