Solve v^2+12v+20=(v+10)(v+2)

$$v ^ { 2 } + 12 v + 20 = ( v + 10 ) ( v + 2 )$$

Solve for v (complex solution)

$$v\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply v+10 by v+2 and combine like terms.

$$v^{2}+12v+20=v^{2}+12v+20$$

Subtract v^{2} from both sides.

$$v^{2}+12v+20-v^{2}=12v+20$$

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

$$12v+20=12v+20$$

Subtract 12v from both sides.

$$12v+20-12v=20$$

Combine 12v and -12v to get 0.

$$20=20$$

Compare 20 and 20.

$$\text{true}$$

This is true for any v.

$$v\in \mathrm{C}$$

Solve for v

$$v\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply v+10 by v+2 and combine like terms.

$$v^{2}+12v+20=v^{2}+12v+20$$

Subtract v^{2} from both sides.

$$v^{2}+12v+20-v^{2}=12v+20$$

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

$$12v+20=12v+20$$

Subtract 12v from both sides.

$$12v+20-12v=20$$

Combine 12v and -12v to get 0.

$$20=20$$

Compare 20 and 20.

$$\text{true}$$

This is true for any v.

$$v\in \mathrm{R}$$