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Solve for uu. \newlineu2+3u=0u^2 + 3u = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlineu=___u = \_\_\_

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Q. Solve for uu. \newlineu2+3u=0u^2 + 3u = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlineu=___u = \_\_\_
  1. Identify Equation: Identify the equation to solve.\newlineWe have the quadratic equation u2+3u=0u^2 + 3u = 0.
  2. Factor Out Common Term: Factor out the common term uu. We can factor uu from both terms in the equation: u(u+3)=0u(u + 3) = 0
  3. Apply Zero Product Property: Apply the zero product property.\newlineIf the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:\newlineu=0u = 0 or u+3=0u + 3 = 0
  4. Solve for uu: Solve each equation for uu.\newlineFirst equation: u=0u = 0\newlineSecond equation: u+3=0u + 3 = 0\newlineSubtract 33 from both sides of the second equation to solve for uu:\newlineu=−3u = -3
  5. Write Solutions: Write the solutions for uu.\newlineThe solutions for the equation u2+3u=0u^2 + 3u = 0 are u=0u = 0 and u=−3u = -3.

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