Solve h(x)=12-5x*g(x)=4x-9

$$h ( x ) = 12 - 5 x \cdot g ( x ) = 4 x - 9$$

Solve for g

$$g=\frac{21-4x}{5x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$12-5x^{2}g=4x-9$$

Subtract 12 from both sides.

$$-5x^{2}g=4x-9-12$$

Subtract 12 from -9 to get -21.

$$-5x^{2}g=4x-21$$

The equation is in standard form.

$$\left(-5x^{2}\right)g=4x-21$$

Divide both sides by -5x^{2}.

$$\frac{\left(-5x^{2}\right)g}{-5x^{2}}=\frac{4x-21}{-5x^{2}}$$

Dividing by -5x^{2} undoes the multiplication by -5x^{2}.

$$g=\frac{4x-21}{-5x^{2}}$$

Divide 4x-21 by -5x^{2}.

$$g=-\frac{4x-21}{5x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{105g+4}+2}{5g}\text{; }x=-\frac{-\sqrt{105g+4}+2}{5g}\text{, }&g\neq 0\\x=\frac{21}{4}\text{, }&g=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{105g+4}+2}{5g}\text{; }x=-\frac{-\sqrt{105g+4}+2}{5g}\text{, }&g\neq 0\text{ and }g\geq -\frac{4}{105}\\x=\frac{21}{4}\text{, }&g=0\end{matrix}\right.$$