Solve (m-2)^2-2^3=(m+1)m-5+sqrt{10sqrt{9}+(-3)(-2)}

$$( m - 2 ) ^ { 2 } - 2 ^ { 3 } = ( m + 1 ) m - 5 + \sqrt { 10 \sqrt { 9 } + ( - 3 ) ( - 2 ) }$$

Solve for m

$$m=-1$$

Steps for Solving Linear Equation

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

$$m^{2}-4m+4-2^{3}=\left(m+1\right)m-5+\sqrt{10\sqrt{9}-3\left(-2\right)}$$

Calculate 2 to the power of 3 and get 8.

$$m^{2}-4m+4-8=\left(m+1\right)m-5+\sqrt{10\sqrt{9}-3\left(-2\right)}$$

Subtract 8 from 4 to get -4.

$$m^{2}-4m-4=\left(m+1\right)m-5+\sqrt{10\sqrt{9}-3\left(-2\right)}$$

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

$$m^{2}-4m-4=m^{2}+m-5+\sqrt{10\sqrt{9}-3\left(-2\right)}$$

Calculate the square root of 9 and get 3.

$$m^{2}-4m-4=m^{2}+m-5+\sqrt{10\times 3-3\left(-2\right)}$$

Multiply 10 and 3 to get 30.

$$m^{2}-4m-4=m^{2}+m-5+\sqrt{30-3\left(-2\right)}$$

Multiply -3 and -2 to get 6.

$$m^{2}-4m-4=m^{2}+m-5+\sqrt{30+6}$$

Add 30 and 6 to get 36.

$$m^{2}-4m-4=m^{2}+m-5+\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$m^{2}-4m-4=m^{2}+m-5+6$$

Add -5 and 6 to get 1.

$$m^{2}-4m-4=m^{2}+m+1$$

Subtract m^{2} from both sides.

$$m^{2}-4m-4-m^{2}=m+1$$

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

$$-4m-4=m+1$$

Subtract m from both sides.

$$-4m-4-m=1$$

Combine -4m and -m to get -5m.

$$-5m-4=1$$

Add 4 to both sides.

$$-5m=1+4$$

Add 1 and 4 to get 5.

$$-5m=5$$

Divide both sides by -5.

$$m=\frac{5}{-5}$$

Divide 5 by -5 to get -1.

$$m=-1$$