Solve the equation by factoring: 2x^(3)+12x^(2)-32 x=0 Answer: x=

Factor GCF: First, we need to factor out the greatest common factor (GCF) from the given equation 2x^3 + 12x^2 - 32x = 0. The GCF is 2x, so we factor it out from each term. 2x(x^2 + 6x - 16) = 0Factor Quadratic Expression: Next, we need to factor the quadratic expression x^2 + 6x - 16. We look for two numbers that multiply to -16 and add up to 6. These numbers are 8 and -2. So, we can write the quadratic as (x + 8)(x - 2).Final Factored Form: Now, we have the factored form of the equation: 2x(x + 8)(x - 2) = 0Solve for x (1): To find the values of x, we set each factor equal to zero and solve for x. First, set 2x = 0, which gives us x = 0.Solve for x (2): Next, set (x + 8) = 0, which gives us x = -8.Solve for x (3): Finally, set (x - 2) = 0, which gives us x = 2.

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Q. Solve the equation by factoring:

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2 x^{3}+12 x^{2}-32 x=0

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Answer:

x=

Factor GCF: First, we need to factor out the greatest common factor (GCF) from the given equation $2x^3 + 12x^2 - 32x = 0$ . The GCF is $2x$ , so we factor it out from each term. $2x(x^2 + 6x - 16) = 0$
Factor Quadratic Expression: Next, we need to factor the quadratic expression $x^2 + 6x - 16$ . We look for two numbers that multiply to $-16$ and add up to $6$ . These numbers are $8$ and $-2$ . So, we can write the quadratic as $(x + 8)(x - 2)$ .
Final Factored Form: Now, we have the factored form of the equation: $2x(x + 8)(x - 2) = 0$
Solve for $x$ ( $1$ ): To find the values of $x$ , we set each factor equal to zero and solve for $x$ . First, set $2x = 0$ , which gives us $x = 0$ .
Solve for $x$ ( $2$ ): Next, set $(x + 8) = 0$ , which gives us $x = -8$ .
Solve for $x$ ( $3$ ): Finally, set $(x - 2) = 0$ , which gives us $x = 2$ .