Solve for n. 6n^(2) = 45 + 3n

Write Equation and Set to Zero: Write down the given equation and set it to zero by moving all terms to one side. 6n^2 - 3n - 45 = 0Factor Quadratic Equation: Factor the quadratic equation if possible. Look for two numbers that multiply to (6 * -45) = -270 and add up to -3. The two numbers that satisfy these conditions are -15 and +18 because (-15) * (+18) = -270 and (-15) + (+18) = +3.Rewrite Using Two Numbers: Rewrite the quadratic equation using the two numbers found in Step 2 to break up the middle term. 6n^2 + 18n - 15n - 45 = 0Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. (6n^2 + 18n) - (15n + 45) = 0Factor Out Common Factors: Factor out the common factors from each group. 6n(n + 3) - 15(n + 3) = 0Factor Out Common Binomial Factor: Factor out the common binomial factor (n + 3). (n + 3)(6n - 15) = 0Set Equal to Zero and Solve: Set each factor equal to zero and solve for n. n + 3 = 0 or 6n - 15 = 0Solve First Equation: Solve the first equation n + 3 = 0 for n. n = -3Solve Second Equation: Solve the second equation 6n - 15 = 0 for n. 6n = 15 n = 15 / 6 n = 5 / 2Write Final Solutions: Write down the final solutions. The solutions are n = -3 and n = 5/2.

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Solve for n. $\newline$ $6n^{2} = 45 + 3n$

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Algebra 2

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Q. Solve for n.

\newline

6n^{2} = 45 + 3n

Write Equation and Set to Zero: Write down the given equation and set it to zero by moving all terms to one side. $\newline$ $6n^2 - 3n - 45 = 0$
Factor Quadratic Equation: Factor the quadratic equation if possible. Look for two numbers that multiply to $(6 \times -45) = -270$ and add up to $-3$ . The two numbers that satisfy these conditions are $-15$ and $+18$ because $(-15) \times (+18) = -270$ and $(-15) + (+18) = +3$ .
Rewrite Using Two Numbers: Rewrite the quadratic equation using the two numbers found in Step $2$ to break up the middle term. $\newline$ $6n^2 + 18n - 15n - 45 = 0$
Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(6n^2 + 18n) - (15n + 45) = 0$
Factor Out Common Factors: Factor out the common factors from each group. $6n(n + 3) - 15(n + 3) = 0$
Factor Out Common Binomial Factor: Factor out the common binomial factor $(n + 3)$ . $(n + 3)(6n - 15) = 0$
Set Equal to Zero and Solve: Set each factor equal to zero and solve for $n$ . $n + 3 = 0$ or $6n - 15 = 0$
Solve First Equation: Solve the first equation $n + 3 = 0$ for $n$ . $n = -3$
Solve Second Equation: Solve the second equation $6n - 15 = 0$ for $n$ . $6n = 15$ $n = \frac{15}{6}$ $n = \frac{5}{2}$
Write Final Solutions: Write down the final solutions. $\newline$ The solutions are $n = -3$ and $n = \frac{5}{2}$ .