Factor completely, 20u^(3)-10u^(2)+18 u=9

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Factor completely,  20u^(3)-10u^(2)+18 u=9

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Identify Common Factor: Step Title: Identify the Common Factor Concise Step Description: Identify the greatest common factor of the terms in the polynomial. Step Calculation: The greatest common factor of 20u^3, 10u^2, and 18u is 2u. Step Output: Greatest common factor: 2uFactor Out Common Factor: Step Title: Factor Out the Greatest Common Factor Concise Step Description: Factor out the greatest common factor from each term in the polynomial. Step Calculation: Factoring out 2u from each term gives us 2u(10u^2 - 5u + 9). Step Output: Factored polynomial: 2u(10u^2 - 5u + 9)Check Further Factoring: Step Title: Check for Further Factoring Concise Step Description: Check if the quadratic expression within the parentheses can be factored further. Step Calculation: The quadratic expression 10u^2 - 5u + 9 does not factor nicely since the discriminant (b^2 - 4ac) is negative: (-5)^2 - 4(10)(9) = 25 - 360 = -335. Step Output: The quadratic expression cannot be factored further.Subtract 9: Step Title: Subtract 9 from Both Sides Concise Step Description: To solve the equation, subtract 9 from both sides to set the equation to zero. Step Calculation: 20u^3 - 10u^2 + 18u - 9 = 0 Step Output: Adjusted equation: 20u^3 - 10u^2 + 18u - 9 = 0Factor Out Common Factor Again: Step Title: Factor Out the Greatest Common Factor Again Concise Step Description: Factor out the greatest common factor from the adjusted equation. Step Calculation: The greatest common factor of 20u^3, 10u^2, 18u, and 9 is 1, which does not change the equation. Step Output: Factored equation: 2u(10u^2 - 5u + 9) - 9 = 0Check Factoring or Solutions: Step Title: Check for Factoring or Solutions Concise Step Description: Check if the adjusted equation can be factored or if there are any solutions. Step Calculation: The equation 2u(10u^2 - 5u + 9) - 9 = 0 does not factor further, and there are no obvious solutions. Step Output: The equation cannot be factored further and has no simple solutions.

Factor completely, $\newline$ $20u^{3}-10u^{2}+18u=9$

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Factor completely,\newline20u3−10u2+18u=920u^{3}-10u^{2}+18u=920u3−10u2+18u=9

Factor completely, $\newline$ $20u^{3}-10u^{2}+18u=9$