6x^3-x^2+17x=2x^2+47x

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Solution for 6x^3-x^2+17x=2x^2+47x equation:


Simplifying
6x3 + -1x2 + 17x = 2x2 + 47x

Reorder the terms:
17x + -1x2 + 6x3 = 2x2 + 47x

Reorder the terms:
17x + -1x2 + 6x3 = 47x + 2x2

Solving
17x + -1x2 + 6x3 = 47x + 2x2

Solving for variable 'x'.

Reorder the terms:
17x + -47x + -1x2 + -2x2 + 6x3 = 47x + 2x2 + -47x + -2x2

Combine like terms: 17x + -47x = -30x
-30x + -1x2 + -2x2 + 6x3 = 47x + 2x2 + -47x + -2x2

Combine like terms: -1x2 + -2x2 = -3x2
-30x + -3x2 + 6x3 = 47x + 2x2 + -47x + -2x2

Reorder the terms:
-30x + -3x2 + 6x3 = 47x + -47x + 2x2 + -2x2

Combine like terms: 47x + -47x = 0
-30x + -3x2 + 6x3 = 0 + 2x2 + -2x2
-30x + -3x2 + 6x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30x + -3x2 + 6x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-10 + -1x + 2x2) = 0

Factor a trinomial.
3x((-2 + -1x)(5 + -2x)) = 0

Ignore the factor 3.

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 '(-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

Subproblem 3

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {0, -2, 2.5}

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