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Solve for $u$ . $\newline$ $20u^2 - 43u = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $u = \_\_$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

u

.

\newline

20u^2 - 43u = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

u = \_\_

Factor GCF: Factor out the greatest common factor (GCF) from the equation $20u^2 - 43u = 0$ . The GCF of $20u^2$ and $43u$ is $u$ . Factor out $u$ from each term. $u(20u - 43) = 0$
Set $u = 0$ : Set each factor equal to zero and solve for $u$ . $\newline$ First, set $u$ equal to zero: $\newline$ $u = 0$ $\newline$ This is one solution.
Solve for $u = \frac{43}{20}$ : Now set the other factor equal to zero and solve for $u$ : $20u - 43 = 0$ Add $43$ to both sides to isolate the term with $u$ : $20u = 43$ Divide both sides by $20$ to solve for $u$ : $u = \frac{43}{20}$ This is the second solution.

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