Solve 2c*3G/2a=3f-4f+3

$$\frac { 2 c \cdot 3 G } { 2 a } = 3 f - 4 f + 3$$

Solve for G

$$\left\{\begin{matrix}G=-\frac{a\left(f-3\right)}{3c}\text{, }&c\neq 0\text{ and }a\neq 0\\G\in \mathrm{R}\text{, }&f=3\text{ and }c=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a.

$$2c\times 3G=3f\times 2a-4f\times 2a+2a\times 3$$

Multiply 2 and 3 to get 6.

$$6cG=3f\times 2a-4f\times 2a+2a\times 3$$

Multiply 3 and 2 to get 6.

$$6cG=6fa-4f\times 2a+2a\times 3$$

Multiply -4 and 2 to get -8.

$$6cG=6fa-8fa+2a\times 3$$

Combine 6fa and -8fa to get -2fa.

$$6cG=-2fa+2a\times 3$$

Multiply 2 and 3 to get 6.

$$6cG=-2fa+6a$$

The equation is in standard form.

$$6cG=6a-2af$$

Divide both sides by 6c.

$$\frac{6cG}{6c}=\frac{6a-2af}{6c}$$

Dividing by 6c undoes the multiplication by 6c.

$$G=\frac{6a-2af}{6c}$$

Divide 6a-2af by 6c.

$$G=\frac{a\left(3-f\right)}{3c}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{3Gc}{f-3}\text{, }&G\neq 0\text{ and }c\neq 0\text{ and }f\neq 3\\a\neq 0\text{, }&\left(c=0\text{ or }G=0\right)\text{ and }f=3\end{matrix}\right.$$

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 2a.

$$2c\times 3G=3f\times 2a-4f\times 2a+2a\times 3$$

Multiply 2 and 3 to get 6.

$$6cG=3f\times 2a-4f\times 2a+2a\times 3$$

Multiply 3 and 2 to get 6.

$$6cG=6fa-4f\times 2a+2a\times 3$$

Multiply -4 and 2 to get -8.

$$6cG=6fa-8fa+2a\times 3$$

Combine 6fa and -8fa to get -2fa.

$$6cG=-2fa+2a\times 3$$

Multiply 2 and 3 to get 6.

$$6cG=-2fa+6a$$

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

$$-2fa+6a=6cG$$

Combine all terms containing a.

$$\left(-2f+6\right)a=6cG$$

The equation is in standard form.

$$\left(6-2f\right)a=6Gc$$

Divide both sides by -2f+6.

$$\frac{\left(6-2f\right)a}{6-2f}=\frac{6Gc}{6-2f}$$

Dividing by -2f+6 undoes the multiplication by -2f+6.

$$a=\frac{6Gc}{6-2f}$$

Divide 6cG by -2f+6.

$$a=\frac{3Gc}{3-f}$$

Variable a cannot be equal to 0.

$$a=\frac{3Gc}{3-f}\text{, }a\neq 0$$