Solve the equation by factoring: 51x^(2)-210 x-3x^(3)=0 Answer: x=

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Solve the equation by factoring:  51x^(2)-210 x-3x^(3)=0 Answer:  x=

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Rearrange Equation: First, we need to rearrange the terms of the equation in descending order of the powers of x. Rearrange the equation: -3x^3 + 51x^2 - 210x = 0Factor Common Factor: Next, we factor out the greatest common factor, which is x in this case. Factor out x: x(-3x^2 + 51x - 210) = 0Factor Quadratic Expression: Now, we need to factor the quadratic expression inside the parentheses. We look for two numbers that multiply to -3 * -210 (which is 630) and add up to 51. The numbers that satisfy these conditions are 63 and -10. Factor the quadratic: x(-3x^2 + 63x - 10x - 210) = 0Group Terms for Factoring: We can now group the terms to factor by grouping. Group the terms: x((-3x^2 + 63x) - (10x + 210)) = 0Factor Common Factors: Factor out the common factors from each group. Factor the first group by 3x and the second by 10: x(3x(-x + 21) - 10(-x + 21)) = 0Factor Out Common Factor: We notice that (-x + 21) is a common factor, so we factor it out. Factor out (-x + 21): x(-x + 21)(3x - 10) = 0Set Factors Equal to Zero: Now we have the equation in factored form, we can find the solutions by setting each factor equal to zero. Set each factor equal to zero: x = 0, -x + 21 = 0, 3x - 10 = 0Solve for x: Solve each equation for x. For x = 0, we already have the solution: x = 0. For -x + 21 = 0, add x to both sides and subtract 21: x = 21. For 3x - 10 = 0, add 10 to both sides and divide by 3: x = 10/3.

Solve the equation by factoring: $\newline$ $51 x^{2}-210 x-3 x^{3}=0$ $\newline$ Answer: $x=$

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Solve the equation by factoring:\newline51x2−210x−3x3=0 51 x^{2}-210 x-3 x^{3}=0 51x2−210x−3x3=0\newlineAnswer: x= x= x=

Solve the equation by factoring: $\newline$ $51 x^{2}-210 x-3 x^{3}=0$ $\newline$ Answer: $x=$