Solve the equation by factoring: 2x^(3)-30x^(2)+108 x=0 Answer: x=

Factor GCF: First, we need to factor out the greatest common factor (GCF) from each term of the equation. The GCF of 2x^3, -30x^2, and 108x is 2x. So we factor out 2x from each term. 2x(x^2 - 15x + 54) = 0Set Factors Equal: Now we have the factored form 2x(x^2 - 15x + 54) = 0. To find the solutions, we set each factor equal to zero. First, set the common factor 2x equal to zero: 2x = 0 x = 0Factor Quadratic: Next, we need to factor the quadratic equation x^2 - 15x + 54. We look for two numbers that multiply to 54 and add up to -15. These numbers are -9 and -6, since (-9) * (-6) = 54 and (-9) + (-6) = -15. So we can write the quadratic as (x - 9)(x - 6).Set Quadratic Factors Equal: Now we set each factor of the quadratic equation equal to zero: x - 9 = 0 and x - 6 = 0. Solving for x gives us two more solutions: x = 9 and x = 6.

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Q. Solve the equation by factoring:

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2 x^{3}-30 x^{2}+108 x=0

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Answer:

x=

Factor GCF: First, we need to factor out the greatest common factor (GCF) from each term of the equation. $\newline$ The GCF of $2x^3$ , $-30x^2$ , and $108x$ is $2x$ . $\newline$ So we factor out $2x$ from each term. $\newline$ $2x(x^2 - 15x + 54) = 0$
Set Factors Equal: Now we have the factored form $2x(x^2 - 15x + 54) = 0$ . $\newline$ To find the solutions, we set each factor equal to zero. $\newline$ First, set the common factor $2x$ equal to zero: $\newline$ $2x = 0$ $\newline$ $x = 0$
Factor Quadratic: Next, we need to factor the quadratic equation $x^2 - 15x + 54$ . We look for two numbers that multiply to $54$ and add up to $-15$ . These numbers are $-9$ and $-6$ , since $(-9) \times (-6) = 54$ and $(-9) + (-6) = -15$ . So we can write the quadratic as $(x - 9)(x - 6)$ .
Set Quadratic Factors Equal: Now we set each factor of the quadratic equation equal to zero: $\newline$ $x - 9 = 0$ and $x - 6 = 0$ . $\newline$ Solving for $x$ gives us two more solutions: $\newline$ $x = 9$ and $x = 6$ .