Solve 5*(-16+Ry)=3*(10-4a)

$$5 \cdot ( - 16 + R y ) = 3 \cdot ( 10 - 4 a )$$

Solve for R (complex solution)

$$\left\{\begin{matrix}R=-\frac{2\left(6a-55\right)}{5y}\text{, }&y\neq 0\\R\in \mathrm{C}\text{, }&a=\frac{55}{6}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by -16+Ry.

$$-80+5Ry=3\left(10-4a\right)$$

Use the distributive property to multiply 3 by 10-4a.

$$-80+5Ry=30-12a$$

Add 80 to both sides.

$$5Ry=30-12a+80$$

Add 30 and 80 to get 110.

$$5Ry=110-12a$$

The equation is in standard form.

$$5yR=110-12a$$

Divide both sides by 5y.

$$\frac{5yR}{5y}=\frac{110-12a}{5y}$$

Dividing by 5y undoes the multiplication by 5y.

$$R=\frac{110-12a}{5y}$$

Divide 110-12a by 5y.

$$R=\frac{2\left(55-6a\right)}{5y}$$

Solve for R

$$\left\{\begin{matrix}R=-\frac{2\left(6a-55\right)}{5y}\text{, }&y\neq 0\\R\in \mathrm{R}\text{, }&a=\frac{55}{6}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by -16+Ry.

$$-80+5Ry=3\left(10-4a\right)$$

Use the distributive property to multiply 3 by 10-4a.

$$-80+5Ry=30-12a$$

Add 80 to both sides.

$$5Ry=30-12a+80$$

Add 30 and 80 to get 110.

$$5Ry=110-12a$$

The equation is in standard form.

$$5yR=110-12a$$

Divide both sides by 5y.

$$\frac{5yR}{5y}=\frac{110-12a}{5y}$$

Dividing by 5y undoes the multiplication by 5y.

$$R=\frac{110-12a}{5y}$$

Divide 110-12a by 5y.

$$R=\frac{2\left(55-6a\right)}{5y}$$

Solve for a

$$a=-\frac{5Ry}{12}+\frac{55}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by -16+Ry.

$$-80+5Ry=3\left(10-4a\right)$$

Use the distributive property to multiply 3 by 10-4a.

$$-80+5Ry=30-12a$$

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

$$30-12a=-80+5Ry$$

Subtract 30 from both sides.

$$-12a=-80+5Ry-30$$

Subtract 30 from -80 to get -110.

$$-12a=-110+5Ry$$

The equation is in standard form.

$$-12a=5Ry-110$$

Divide both sides by -12.

$$\frac{-12a}{-12}=\frac{5Ry-110}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$a=\frac{5Ry-110}{-12}$$

Divide -110+5Ry by -12.

$$a=-\frac{5Ry}{12}+\frac{55}{6}$$