Solve 72^{2}m^2(m+1)^2-64(1+9m^2)(9m^2+18m+8)=0

$$72 ^ { 2 } m ^ { 2 } ( m + 1 ) ^ { 2 } - 64 ( 1 + 9 m ^ { 2 } ) ( 9 m ^ { 2 } + 18 m + 8 ) = 0$$

Solve for m

$$m=-\frac{4}{9}\approx -0.444444444$$

Steps for Solving Linear Equation

Calculate 72 to the power of 2 and get 5184.

$$5184m^{2}\left(m+1\right)^{2}-64\left(1+9m^{2}\right)\left(9m^{2}+18m+8\right)=0$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+1\right)^{2}.

$$5184m^{2}\left(m^{2}+2m+1\right)-64\left(1+9m^{2}\right)\left(9m^{2}+18m+8\right)=0$$

Use the distributive property to multiply 5184m^{2} by m^{2}+2m+1.

$$5184m^{4}+10368m^{3}+5184m^{2}-64\left(1+9m^{2}\right)\left(9m^{2}+18m+8\right)=0$$

Use the distributive property to multiply -64 by 1+9m^{2}.

$$5184m^{4}+10368m^{3}+5184m^{2}+\left(-64-576m^{2}\right)\left(9m^{2}+18m+8\right)=0$$

Use the distributive property to multiply -64-576m^{2} by 9m^{2}+18m+8 and combine like terms.

$$5184m^{4}+10368m^{3}+5184m^{2}-5184m^{2}-1152m-512-5184m^{4}-10368m^{3}=0$$

Combine 5184m^{2} and -5184m^{2} to get 0.

$$5184m^{4}+10368m^{3}-1152m-512-5184m^{4}-10368m^{3}=0$$

Combine 5184m^{4} and -5184m^{4} to get 0.

$$10368m^{3}-1152m-512-10368m^{3}=0$$

Combine 10368m^{3} and -10368m^{3} to get 0.

$$-1152m-512=0$$

Add 512 to both sides. Anything plus zero gives itself.

$$-1152m=512$$

Divide both sides by -1152.

$$m=\frac{512}{-1152}$$

Reduce the fraction \frac{512}{-1152} to lowest terms by extracting and canceling out 128.

$$m=-\frac{4}{9}$$