Question 55488
First, let's work on the left hand side of your equation, the 4^2x+1
This means, for instance, to see if it can be simplified at all.



16 
Multiply x and 16 

Multiply x and 1 




The x just gets copied along. 

x 
x 



16x 


16x+1 
So, all-in-all, the left hand side of your equation can be written as: 16x+1 


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Now, let's work on the right hand side of your equation, the 2^3x+6



8 
Multiply x and 8 

Multiply x and 1 



The x just gets copied along. 

x 
x 


8x 


8x+6 
The right hand side of your equation can be written as: 8x+6 


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So with these (any) simplifications, the equation we'll set out to solve is:

16x+1 = 8x+6 


Move the 1 to the right hand side by subtracting 1 from both sides, like this:


From the left hand side:
1 - 1 = 0 



16x 
From the right hand side:
6 - 1 = 5 



5+8x 

Now, the equation reads:
16x = 5+8x 

Move the 8x to the left hand side by subtracting 8x from both sides, like this:
From the left hand side:
16x - 8x = 8x 


8x 
From the right hand side:
8x - 8x = 0 



5 

Now, the equation reads:
8x = 5 
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.



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The last step is to divide both sides of the equation by 8 like this:

To divide x by 1 




The x just gets copied along in the numerator. 


x 
8x ÷ 8 = x 


5 ÷ 8 = 5/8 or 0.625

The solution to your equation is:
x = 5/8 or 0.625