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Solve for $k$ . $\newline$ $21k^2 + 23k = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $k =$ ____

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

k

.

\newline

21k^2 + 23k = 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

k =

____

Factor GCF: Factor out the greatest common factor (GCF) from the equation $21k^2 + 23k = 0$ . The GCF of $21k^2$ and $23k$ is $k$ . Factor out $k$ from each term. $k(21k + 23) = 0$
Set Equal Solve: Set each factor equal to zero and solve for $k$ . $\newline$ First, set $k$ equal to zero: $\newline$ $k = 0$ $\newline$ Then, set the other factor equal to zero: $\newline$ $21k + 23 = 0$
Solve $21k + 23$ : Solve the equation $21k + 23 = 0$ for $k$ . $\newline$ Subtract $23$ from both sides of the equation to isolate the term with $k$ . $\newline$ $21k + 23 - 23 = 0 - 23$ $\newline$ $21k = -23$ $\newline$ Divide both sides by $21$ to solve for $k$ . $\newline$ $k = -\frac{23}{21}$ $\newline$ Simplify the fraction. $\newline$ $21k + 23 = 0$ $0$

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