Solve (x+5)(x-A)=x^2-Bx-70

$$( x + 5 ) ( x - A ) = x ^ { 2 } - B x - 70$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{Bx+5x+70}{x+5}\text{, }&x\neq -5\\A\in \mathrm{C}\text{, }&x=-5\text{ and }B=9\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+5 by x-A.

$$x^{2}-xA+5x-5A=x^{2}-Bx-70$$

Subtract x^{2} from both sides.

$$-xA+5x-5A=x^{2}-Bx-70-x^{2}$$

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

$$-xA+5x-5A=-Bx-70$$

Subtract 5x from both sides.

$$-xA-5A=-Bx-70-5x$$

Combine all terms containing A.

$$\left(-x-5\right)A=-Bx-70-5x$$

The equation is in standard form.

$$\left(-x-5\right)A=-Bx-5x-70$$

Divide both sides by -x-5.

$$\frac{\left(-x-5\right)A}{-x-5}=\frac{-Bx-5x-70}{-x-5}$$

Dividing by -x-5 undoes the multiplication by -x-5.

$$A=\frac{-Bx-5x-70}{-x-5}$$

Divide -5x-70-Bx by -x-5.

$$A=\frac{Bx+5x+70}{x+5}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=\frac{Ax-5x+5A-70}{x}\text{, }&x\neq 0\\B\in \mathrm{C}\text{, }&A=14\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+5 by x-A.

$$x^{2}-xA+5x-5A=x^{2}-Bx-70$$

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

$$x^{2}-Bx-70=x^{2}-xA+5x-5A$$

Subtract x^{2} from both sides.

$$-Bx-70=x^{2}-xA+5x-5A-x^{2}$$

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

$$-Bx-70=-xA+5x-5A$$

Add 70 to both sides.

$$-Bx=-xA+5x-5A+70$$

The equation is in standard form.

$$\left(-x\right)B=70-5A+5x-Ax$$

Divide both sides by -x.

$$\frac{\left(-x\right)B}{-x}=\frac{70-5A+5x-Ax}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$B=\frac{70-5A+5x-Ax}{-x}$$

Divide -xA+5x-5A+70 by -x.

$$B=A+\frac{5A-70}{x}-5$$

Solve for A

$$\left\{\begin{matrix}A=\frac{Bx+5x+70}{x+5}\text{, }&x\neq -5\\A\in \mathrm{R}\text{, }&x=-5\text{ and }B=9\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+5 by x-A.

$$x^{2}-xA+5x-5A=x^{2}-Bx-70$$

Subtract x^{2} from both sides.

$$-xA+5x-5A=x^{2}-Bx-70-x^{2}$$

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

$$-xA+5x-5A=-Bx-70$$

Subtract 5x from both sides.

$$-xA-5A=-Bx-70-5x$$

Combine all terms containing A.

$$\left(-x-5\right)A=-Bx-70-5x$$

The equation is in standard form.

$$\left(-x-5\right)A=-Bx-5x-70$$

Divide both sides by -x-5.

$$\frac{\left(-x-5\right)A}{-x-5}=\frac{-Bx-5x-70}{-x-5}$$

Dividing by -x-5 undoes the multiplication by -x-5.

$$A=\frac{-Bx-5x-70}{-x-5}$$

Divide -Bx-70-5x by -x-5.

$$A=\frac{Bx+5x+70}{x+5}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{Ax-5x+5A-70}{x}\text{, }&x\neq 0\\B\in \mathrm{R}\text{, }&A=14\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+5 by x-A.

$$x^{2}-xA+5x-5A=x^{2}-Bx-70$$

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

$$x^{2}-Bx-70=x^{2}-xA+5x-5A$$

Subtract x^{2} from both sides.

$$-Bx-70=x^{2}-xA+5x-5A-x^{2}$$

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

$$-Bx-70=-xA+5x-5A$$

Add 70 to both sides.

$$-Bx=-xA+5x-5A+70$$

The equation is in standard form.

$$\left(-x\right)B=70-5A+5x-Ax$$

Divide both sides by -x.

$$\frac{\left(-x\right)B}{-x}=\frac{70-5A+5x-Ax}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$B=\frac{70-5A+5x-Ax}{-x}$$

Divide -xA+5x-5A+70 by -x.

$$B=A+\frac{5A-70}{x}-5$$