Solve 6+84*4:(21*4-17*28:n+5*8):3=8

$$6 + 84 \times 4 : ( 21 \times 4 - 17 \times 28 : n + 5 \times 8 ) : 3 = 8$$

Solve for n

$$n=7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$18+\frac{84\times 4}{21\times 4-\frac{17\times 28}{n}+5\times 8}=24$$

Multiply 84 and 4 to get 336.

$$18+\frac{336}{21\times 4-\frac{17\times 28}{n}+5\times 8}=24$$

Do the multiplications.

$$18+\frac{336}{84-\frac{17\times 28}{n}+40}=24$$

Multiply 17 and 28 to get 476.

$$18+\frac{336}{84-\frac{476}{n}+40}=24$$

Add 84 and 40 to get 124.

$$18+\frac{336}{124-\frac{476}{n}}=24$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 124 times \frac{n}{n}.

$$18+\frac{336}{\frac{124n}{n}-\frac{476}{n}}=24$$

Since \frac{124n}{n} and \frac{476}{n} have the same denominator, subtract them by subtracting their numerators.

$$18+\frac{336}{\frac{124n-476}{n}}=24$$

Variable n cannot be equal to 0 since division by zero is not defined. Divide 336 by \frac{124n-476}{n} by multiplying 336 by the reciprocal of \frac{124n-476}{n}.

$$18+\frac{336n}{124n-476}=24$$

Factor the expressions that are not already factored in \frac{336n}{124n-476}.

$$18+\frac{336n}{4\left(31n-119\right)}=24$$

Cancel out 4 in both numerator and denominator.

$$18+\frac{84n}{31n-119}=24$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 18 times \frac{31n-119}{31n-119}.

$$\frac{18\left(31n-119\right)}{31n-119}+\frac{84n}{31n-119}=24$$

Since \frac{18\left(31n-119\right)}{31n-119} and \frac{84n}{31n-119} have the same denominator, add them by adding their numerators.

$$\frac{18\left(31n-119\right)+84n}{31n-119}=24$$

Do the multiplications in 18\left(31n-119\right)+84n.

$$\frac{558n-2142+84n}{31n-119}=24$$

Combine like terms in 558n-2142+84n.

$$\frac{642n-2142}{31n-119}=24$$

Variable n cannot be equal to \frac{119}{31} since division by zero is not defined. Multiply both sides of the equation by 31n-119.

$$642n-2142=24\left(31n-119\right)$$

Use the distributive property to multiply 24 by 31n-119.

$$642n-2142=744n-2856$$

Subtract 744n from both sides.

$$642n-2142-744n=-2856$$

Combine 642n and -744n to get -102n.

$$-102n-2142=-2856$$

Add 2142 to both sides.

$$-102n=-2856+2142$$

Add -2856 and 2142 to get -714.

$$-102n=-714$$

Divide both sides by -102.

$$n=\frac{-714}{-102}$$

Divide -714 by -102 to get 7.

$$n=7$$