Final answer:
The student likely made a typo in their mathematics equation, and without the correct equation, we can't solve it accurately. Factoring involves breaking down expressions to simplify and solve for variables.
Step-by-step explanation:
The student appears to have typed a mathematics question related to solving an equation, but there seems to be a typographical error in their question: '3n- + 40 = 23n solved by factoring'.
It could be that they are asking how to solve for 'n' in an equation similar to '3n + 40 = 23n', but without the correct equation, we can't provide a factual solution. However, if we were to factor an equation of this form, we would subtract '3n' from both sides to get '40 = 20n', and then divide both sides by '20' to solve for 'n'.
Factoring in mathematics typically involves breaking down an expression into simpler terms or finding the prime factors of a number. In the context of equations, it can involve rearranging terms to group like terms together and simplify the equation to solve for an unknown variable. It's essential to ensure that the equation provided is accurate before attempting to factor or solve it.
To solve the equation 3n- + 40 = 23n using factoring, we need to bring all the terms to one side of the equation and set it equal to zero. Subtract 23n from both sides to get -20n + 40 = 0.
Now, factor out a common factor of 20 to get 20(-n + 2) = 0. Setting each factor equal to zero gives us -n + 2 = 0. Finally, solve for n by subtracting 2 from both sides to get -n = -2, and then multiplying both sides by -1 to get n = 2.