Solve the equation by factoring: 2x^(3)-6x^(2)-20 x=0 Answer: x=

Factor out GCF: First, we need to factor out the greatest common factor (GCF) from the given cubic equation 2x^3 - 6x^2 - 20x = 0. The GCF of 2x^3, -6x^2, and -20x is 2x. So we factor 2x out of each term. 2x(x^2 - 3x - 10) = 0Factor quadratic equation: Now we need to factor the quadratic equation x^2 - 3x - 10. We look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and +2. So we can write the quadratic as (x - 5)(x + 2). 2x(x - 5)(x + 2) = 0Set factor equal to zero: To find the roots of the equation, we set each factor equal to zero and solve for x. First, we set the factor 2x equal to zero: 2x = 0 x = 0Set factor equal to zero: Next, we set the factor (x - 5) equal to zero: x - 5 = 0 x = 5Set factor equal to zero: Finally, we set the factor (x + 2) equal to zero: x + 2 = 0 x = -2

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Q. Solve the equation by factoring:

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2 x^{3}-6 x^{2}-20 x=0

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Answer:

x=

Factor out GCF: First, we need to factor out the greatest common factor (GCF) from the given cubic equation $2x^3 - 6x^2 - 20x = 0$ . The GCF of $2x^3$ , $-6x^2$ , and $-20x$ is $2x$ . So we factor $2x$ out of each term. $2x(x^2 - 3x - 10) = 0$
Factor quadratic equation: Now we need to factor the quadratic equation $x^2 - 3x - 10$ . We look for two numbers that multiply to $-10$ and add up to $-3$ . These numbers are $-5$ and $+2$ . So we can write the quadratic as $(x - 5)(x + 2)$ . $2x(x - 5)(x + 2) = 0$
Set factor equal to zero: To find the roots of the equation, we set each factor equal to zero and solve for $x$ . First, we set the factor $2x$ equal to zero: $2x = 0$ $x = 0$
Set factor equal to zero: Next, we set the factor $(x - 5)$ equal to zero: $\newline$ $x - 5 = 0$ $\newline$ $x = 5$
Set factor equal to zero: Finally, we set the factor $(x + 2)$ equal to zero: $\newline$ $x + 2 = 0$ $\newline$ $x = -2$