Solve (-2m^2+4-12m)^2-4(1+m^2)(m^2+12m+31)=0

$$( - 2 m ^ { 2 } + 4 - 12 m ) ^ { 2 } - 4 ( 1 + m ^ { 2 } ) ( m ^ { 2 } + 12 m + 31 ) = 0$$

Solve for m

$$m=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

Square -2m^{2}+4-12m.

$$4m^{4}+48m^{3}+128m^{2}-96m+16-4\left(1+m^{2}\right)\left(m^{2}+12m+31\right)=0$$

Use the distributive property to multiply -4 by 1+m^{2}.

$$4m^{4}+48m^{3}+128m^{2}-96m+16+\left(-4-4m^{2}\right)\left(m^{2}+12m+31\right)=0$$

Use the distributive property to multiply -4-4m^{2} by m^{2}+12m+31 and combine like terms.

$$4m^{4}+48m^{3}+128m^{2}-96m+16-128m^{2}-48m-124-4m^{4}-48m^{3}=0$$

Combine 128m^{2} and -128m^{2} to get 0.

$$4m^{4}+48m^{3}-96m+16-48m-124-4m^{4}-48m^{3}=0$$

Combine -96m and -48m to get -144m.

$$4m^{4}+48m^{3}-144m+16-124-4m^{4}-48m^{3}=0$$

Subtract 124 from 16 to get -108.

$$4m^{4}+48m^{3}-144m-108-4m^{4}-48m^{3}=0$$

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

$$48m^{3}-144m-108-48m^{3}=0$$

Combine 48m^{3} and -48m^{3} to get 0.

$$-144m-108=0$$

Add 108 to both sides. Anything plus zero gives itself.

$$-144m=108$$

Divide both sides by -144.

$$m=\frac{108}{-144}$$

Reduce the fraction \frac{108}{-144} to lowest terms by extracting and canceling out 36.

$$m=-\frac{3}{4}$$