Solve f(x)=x^2+5x+6quadyquadg(x)=x^2-3x-10

$$f ( x ) = x ^ { 2 } + 5 x + 6 \quad y \quad g ( x ) = x ^ { 2 } - 3 x - 10$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{4x+5}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\g\in \mathrm{C}\text{, }&x=-\frac{5}{4}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$5x+6ygx=x^{2}-3x-10-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$5x+6ygx=-3x-10$$

Subtract 5x from both sides.

$$6ygx=-3x-10-5x$$

Combine -3x and -5x to get -8x.

$$6ygx=-8x-10$$

The equation is in standard form.

$$6xyg=-8x-10$$

Divide both sides by 6yx.

$$\frac{6xyg}{6xy}=\frac{-8x-10}{6xy}$$

Dividing by 6yx undoes the multiplication by 6yx.

$$g=\frac{-8x-10}{6xy}$$

Divide -10-8x by 6yx.

$$g=-\frac{4x+5}{3xy}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{4x+5}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\g\in \mathrm{R}\text{, }&x=-\frac{5}{4}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$5x+6ygx=x^{2}-3x-10-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$5x+6ygx=-3x-10$$

Subtract 5x from both sides.

$$6ygx=-3x-10-5x$$

Combine -3x and -5x to get -8x.

$$6ygx=-8x-10$$

The equation is in standard form.

$$6xyg=-8x-10$$

Divide both sides by 6yx.

$$\frac{6xyg}{6xy}=\frac{-8x-10}{6xy}$$

Dividing by 6yx undoes the multiplication by 6yx.

$$g=\frac{-8x-10}{6xy}$$

Divide -8x-10 by 6yx.

$$g=-\frac{4x+5}{3xy}$$

Solve for x

$$x=-\frac{5}{3gy+4}$$

$$g=0\text{ or }y\neq -\frac{4}{3g}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$x^{2}+5x+6ygx-x^{2}=-3x-10$$

Combine x^{2} and -x^{2} to get 0.

$$5x+6ygx=-3x-10$$

Add 3x to both sides.

$$5x+6ygx+3x=-10$$

Combine 5x and 3x to get 8x.

$$8x+6ygx=-10$$

Combine all terms containing x.

$$\left(8+6yg\right)x=-10$$

The equation is in standard form.

$$\left(6gy+8\right)x=-10$$

Divide both sides by 6gy+8.

$$\frac{\left(6gy+8\right)x}{6gy+8}=-\frac{10}{6gy+8}$$

Dividing by 6gy+8 undoes the multiplication by 6gy+8.

$$x=-\frac{10}{6gy+8}$$

Divide -10 by 6gy+8.

$$x=-\frac{5}{3gy+4}$$