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To solve the equation *a*⋅(*n*+*y*)=10*y*+32, you will need to follow these steps:

Step 1: Distribute the *a* to the terms inside the parentheses:

*a*⋅*n*+*a*⋅*y*=10*y*+32

Step 2: Rearrange the equation by grouping the terms with *y* on one side and the terms without *y* on the other side:

*a*⋅*y* - 10*y* = 32 - *a*⋅*n*

Step 3: Factor out *y* on the left side of the equation:

(*a* - 10)⋅*y* = 32 - *a*⋅*n*

Step 4: Divide both sides of the equation by the factor (*a* - 10) to isolate *y*:

*y* = (32 - *a*⋅*n*)/(*a* - 10)

So, the solution to the equation *a*⋅(*n*+*y*)=10*y*+32 is *y* = (32 - *a*⋅*n*)/(*a* - 10).

This equation is an example of a linear equation with two variables, *n* and *y*. When solving linear equations, the goal is to isolate the variable you are solving for on one side of the equation. In this case, we wanted to isolate *y*.

To isolate *y*, we first multiplied *a* by both *n* and *y*. Then, we rearranged the equation so that the terms with *y* were grouped on one side and the terms without *y* were on the other side.

Then, we factored out *y* on the left side of the equation and divided both sides of the equation by the factor (*a* - 10) to solve for *y*.