Solve =[-2(m+1)]^2-2(m^2-1)=16+8x+m^2-1

$$= [ - 2 ( m + 1 ) ] ^ { 2 } - 2 ( m ^ { 2 } - 1 ) = 16 + 8 x + m ^ { 2 } - 1$$

Solve for x

$$x=\frac{\left(m-1\right)\left(m+9\right)}{8}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by m+1.

$$\left(-2m-2\right)^{2}-2\left(m^{2}-1\right)=16+8x+m^{2}-1$$

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

$$4m^{2}+8m+4-2\left(m^{2}-1\right)=16+8x+m^{2}-1$$

Use the distributive property to multiply -2 by m^{2}-1.

$$4m^{2}+8m+4-2m^{2}+2=16+8x+m^{2}-1$$

Combine 4m^{2} and -2m^{2} to get 2m^{2}.

$$2m^{2}+8m+4+2=16+8x+m^{2}-1$$

Add 4 and 2 to get 6.

$$2m^{2}+8m+6=16+8x+m^{2}-1$$

Subtract 1 from 16 to get 15.

$$2m^{2}+8m+6=15+8x+m^{2}$$

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

$$15+8x+m^{2}=2m^{2}+8m+6$$

Subtract 15 from both sides.

$$8x+m^{2}=2m^{2}+8m+6-15$$

Subtract 15 from 6 to get -9.

$$8x+m^{2}=2m^{2}+8m-9$$

Subtract m^{2} from both sides.

$$8x=2m^{2}+8m-9-m^{2}$$

Combine 2m^{2} and -m^{2} to get m^{2}.

$$8x=m^{2}+8m-9$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{\left(m-1\right)\left(m+9\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{\left(m-1\right)\left(m+9\right)}{8}$$

Solve for m (complex solution)

$$m=\sqrt{8x+25}-4$$

$$m=-\sqrt{8x+25}-4$$

Solve for m

$$m=\sqrt{8x+25}-4$$

$$m=-\sqrt{8x+25}-4\text{, }x\geq -\frac{25}{8}$$