Solve 7/9*2*9-6/0+20=2(9-b/2n+0+1)*7/a-14

$$\frac { 7 } { 9 } \times 2 \times \frac { 9 - 6 } { 0 + 20 } = 2 ( \frac { 9 - b } { 2 n + 0 } + 1 ) \times \frac { 7 } { a } - 14$$

Solve for a

$$a=\frac{30\left(2n-b+9\right)}{61n}$$

$$b\neq 2n+9\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 18an, the least common multiple of 9,2n+0,a.

$$\frac{7}{9}\times 2\times \frac{9}{10}an\left(9-6\right)=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Multiply \frac{7}{9} and 2 to get \frac{14}{9}.

$$\frac{14}{9}\times \frac{9}{10}an\left(9-6\right)=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Multiply \frac{14}{9} and \frac{9}{10} to get \frac{7}{5}.

$$\frac{7}{5}an\left(9-6\right)=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Subtract 6 from 9 to get 3.

$$\frac{7}{5}an\times 3=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Multiply \frac{7}{5} and 3 to get \frac{21}{5}.

$$\frac{21}{5}an=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Anything plus zero gives itself.

$$\frac{21}{5}an=2\left(\frac{9-b}{2n}+1\right)\times 18n\times 7+18an\left(-14\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2n}{2n}.

$$\frac{21}{5}an=2\left(\frac{9-b}{2n}+\frac{2n}{2n}\right)\times 18n\times 7+18an\left(-14\right)$$

Since \frac{9-b}{2n} and \frac{2n}{2n} have the same denominator, add them by adding their numerators.

$$\frac{21}{5}an=2\times \frac{9-b+2n}{2n}\times 18n\times 7+18an\left(-14\right)$$

Combine like terms in 9-b+2n.

$$\frac{21}{5}an=2\times \frac{9+2n-b}{2n}\times 18n\times 7+18an\left(-14\right)$$

Multiply 2 and 18 to get 36.

$$\frac{21}{5}an=36\times \frac{9+2n-b}{2n}n\times 7+18an\left(-14\right)$$

Multiply 36 and 7 to get 252.

$$\frac{21}{5}an=252\times \frac{9+2n-b}{2n}n+18an\left(-14\right)$$

Express 252\times \frac{9+2n-b}{2n} as a single fraction.

$$\frac{21}{5}an=\frac{252\left(9+2n-b\right)}{2n}n+18an\left(-14\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{21}{5}an=\frac{126\left(2n-b+9\right)}{n}n+18an\left(-14\right)$$

Express \frac{126\left(2n-b+9\right)}{n}n as a single fraction.

$$\frac{21}{5}an=\frac{126\left(2n-b+9\right)n}{n}+18an\left(-14\right)$$

Cancel out n in both numerator and denominator.

$$\frac{21}{5}an=126\left(2n-b+9\right)+18an\left(-14\right)$$

Use the distributive property to multiply 126 by 2n-b+9.

$$\frac{21}{5}an=252n-126b+1134+18an\left(-14\right)$$

Multiply 18 and -14 to get -252.

$$\frac{21}{5}an=252n-126b+1134-252an$$

Add 252an to both sides.

$$\frac{21}{5}an+252an=252n-126b+1134$$

Combine \frac{21}{5}an and 252an to get \frac{1281}{5}an.

$$\frac{1281}{5}an=252n-126b+1134$$

The equation is in standard form.

$$\frac{1281n}{5}a=252n-126b+1134$$

Divide both sides by \frac{1281}{5}n.

$$\frac{5\times \frac{1281n}{5}a}{1281n}=\frac{5\left(252n-126b+1134\right)}{1281n}$$

Dividing by \frac{1281}{5}n undoes the multiplication by \frac{1281}{5}n.

$$a=\frac{5\left(252n-126b+1134\right)}{1281n}$$

Divide 252n-126b+1134 by \frac{1281}{5}n.

$$a=\frac{30\left(2n-b+9\right)}{61n}$$

Variable a cannot be equal to 0.

$$a=\frac{30\left(2n-b+9\right)}{61n}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{61an}{30}+2n+9$$

$$n\neq 0\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18an, the least common multiple of 9,2n+0,a.

$$\frac{7}{9}\times 2\times \frac{9}{10}an\left(9-6\right)=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Multiply \frac{7}{9} and 2 to get \frac{14}{9}.

$$\frac{14}{9}\times \frac{9}{10}an\left(9-6\right)=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Multiply \frac{14}{9} and \frac{9}{10} to get \frac{7}{5}.

$$\frac{7}{5}an\left(9-6\right)=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Subtract 6 from 9 to get 3.

$$\frac{7}{5}an\times 3=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Multiply \frac{7}{5} and 3 to get \frac{21}{5}.

$$\frac{21}{5}an=2\left(\frac{9-b}{2n+0}+1\right)\times 18n\times 7+18an\left(-14\right)$$

Anything plus zero gives itself.

$$\frac{21}{5}an=2\left(\frac{9-b}{2n}+1\right)\times 18n\times 7+18an\left(-14\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2n}{2n}.

$$\frac{21}{5}an=2\left(\frac{9-b}{2n}+\frac{2n}{2n}\right)\times 18n\times 7+18an\left(-14\right)$$

Since \frac{9-b}{2n} and \frac{2n}{2n} have the same denominator, add them by adding their numerators.

$$\frac{21}{5}an=2\times \frac{9-b+2n}{2n}\times 18n\times 7+18an\left(-14\right)$$

Multiply 2 and 18 to get 36.

$$\frac{21}{5}an=36\times \frac{9-b+2n}{2n}n\times 7+18an\left(-14\right)$$

Multiply 36 and 7 to get 252.

$$\frac{21}{5}an=252\times \frac{9-b+2n}{2n}n+18an\left(-14\right)$$

Express 252\times \frac{9-b+2n}{2n} as a single fraction.

$$\frac{21}{5}an=\frac{252\left(9-b+2n\right)}{2n}n+18an\left(-14\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{21}{5}an=\frac{126\left(2n-b+9\right)}{n}n+18an\left(-14\right)$$

Express \frac{126\left(2n-b+9\right)}{n}n as a single fraction.

$$\frac{21}{5}an=\frac{126\left(2n-b+9\right)n}{n}+18an\left(-14\right)$$

Cancel out n in both numerator and denominator.

$$\frac{21}{5}an=126\left(2n-b+9\right)+18an\left(-14\right)$$

Use the distributive property to multiply 126 by 2n-b+9.

$$\frac{21}{5}an=252n-126b+1134+18an\left(-14\right)$$

Multiply 18 and -14 to get -252.

$$\frac{21}{5}an=252n-126b+1134-252an$$

Swap sides so that all variable terms are on the left hand side.

$$252n-126b+1134-252an=\frac{21}{5}an$$

Subtract 252n from both sides.

$$-126b+1134-252an=\frac{21}{5}an-252n$$

Subtract 1134 from both sides.

$$-126b-252an=\frac{21}{5}an-252n-1134$$

Add 252an to both sides.

$$-126b=\frac{21}{5}an-252n-1134+252an$$

Combine \frac{21}{5}an and 252an to get \frac{1281}{5}an.

$$-126b=\frac{1281}{5}an-252n-1134$$

The equation is in standard form.

$$-126b=\frac{1281an}{5}-252n-1134$$

Divide both sides by -126.

$$\frac{-126b}{-126}=\frac{\frac{1281an}{5}-252n-1134}{-126}$$

Dividing by -126 undoes the multiplication by -126.

$$b=\frac{\frac{1281an}{5}-252n-1134}{-126}$$

Divide \frac{1281an}{5}-252n-1134 by -126.

$$b=-\frac{61an}{30}+2n+9$$