Solve (a+d)^2=a(a+3d)

$$( a + d ) ^ { 2 } = a ( a + 3 d )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=d\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(a+d\right)^{2}.

$$a^{2}+2ad+d^{2}=a\left(a+3d\right)$$

Use the distributive property to multiply a by a+3d.

$$a^{2}+2ad+d^{2}=a^{2}+3ad$$

Subtract a^{2} from both sides.

$$a^{2}+2ad+d^{2}-a^{2}=3ad$$

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

$$2ad+d^{2}=3ad$$

Subtract 3ad from both sides.

$$2ad+d^{2}-3ad=0$$

Combine 2ad and -3ad to get -ad.

$$-ad+d^{2}=0$$

Subtract d^{2} from both sides. Anything subtracted from zero gives its negation.

$$-ad=-d^{2}$$

Cancel out -1 on both sides.

$$ad=d^{2}$$

The equation is in standard form.

$$da=d^{2}$$

Divide both sides by d.

$$\frac{da}{d}=\frac{d^{2}}{d}$$

Dividing by d undoes the multiplication by d.

$$a=\frac{d^{2}}{d}$$

Divide d^{2} by d.

$$a=d$$

Solve for a

$$\left\{\begin{matrix}\\a=d\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(a+d\right)^{2}.

$$a^{2}+2ad+d^{2}=a\left(a+3d\right)$$

Use the distributive property to multiply a by a+3d.

$$a^{2}+2ad+d^{2}=a^{2}+3ad$$

Subtract a^{2} from both sides.

$$a^{2}+2ad+d^{2}-a^{2}=3ad$$

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

$$2ad+d^{2}=3ad$$

Subtract 3ad from both sides.

$$2ad+d^{2}-3ad=0$$

Combine 2ad and -3ad to get -ad.

$$-ad+d^{2}=0$$

Subtract d^{2} from both sides. Anything subtracted from zero gives its negation.

$$-ad=-d^{2}$$

Cancel out -1 on both sides.

$$ad=d^{2}$$

The equation is in standard form.

$$da=d^{2}$$

Divide both sides by d.

$$\frac{da}{d}=\frac{d^{2}}{d}$$

Dividing by d undoes the multiplication by d.

$$a=\frac{d^{2}}{d}$$

Divide d^{2} by d.

$$a=d$$

Solve for d

$$d=a$$

$$d=0$$