Solve the equation by factoring: 60 x-24x^(2)-3x^(3)=0 Answer: x=

Factor GCF: First, we need to factor out the greatest common factor from the given equation 60x - 24x^2 - 3x^3 = 0. The greatest common factor is 3x, so we factor it out. 3x(20 - 8x - x^2) = 0Rearrange Terms: Next, we need to rearrange the terms inside the parentheses in descending order of the powers of x. 3x(-x^2 - 8x + 20) = 0Factor Quadratic: Now, we factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to -20 and add up to -8. These numbers are -10 and +2. So, we can write the quadratic as (-x + 2)(x - 10). 3x(-x + 2)(x - 10) = 0Find Roots (1): We have the factored form of the equation. Now, we can find the roots by setting each factor equal to zero. First, set the factor 3x equal to zero: 3x = 0 x = 0Find Roots (2): Next, set the factor (-x + 2) equal to zero: -x + 2 = 0 x = 2Find Roots (3): Finally, set the factor (x - 10) equal to zero: x - 10 = 0 x = 10

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Q. Solve the equation by factoring:

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60 x-24 x^{2}-3 x^{3}=0

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Answer:

x=

Factor GCF: First, we need to factor out the greatest common factor from the given equation $60x - 24x^2 - 3x^3 = 0$ . The greatest common factor is $3x$ , so we factor it out. $3x(20 - 8x - x^2) = 0$
Rearrange Terms: Next, we need to rearrange the terms inside the parentheses in descending order of the powers of $x$ . $3x(-x^2 - 8x + 20) = 0$
Factor Quadratic: Now, we factor the quadratic expression inside the parentheses. $\newline$ We are looking for two numbers that multiply to $-20$ and add up to $-8$ . These numbers are $-10$ and $+2$ . $\newline$ So, we can write the quadratic as $(-x + 2)(x - 10)$ . $\newline$ $3x(-x + 2)(x - 10) = 0$
Find Roots ( $1$ ): We have the factored form of the equation. Now, we can find the roots by setting each factor equal to zero. $\newline$ First, set the factor $3x$ equal to zero: $\newline$ $3x = 0$ $\newline$ $x = 0$
Find Roots ( $2$ ): Next, set the factor $(-x + 2)$ equal to zero: $\newline$ $-x + 2 = 0$ $\newline$ $x = 2$
Find Roots ( $3$ ): Finally, set the factor $x - 10$ equal to zero: $\newline$ $x - 10 = 0$ $\newline$ $x = 10$