Solve (2m-1)^2-(2m+5)^2=24

$$( 2 m - 1 ) ^ { 2 } - ( 2 m + 5 ) ^ { 2 } = 24$$

Solve for m

$$m=-2$$

Steps for Solving Linear Equation

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

$$4m^{2}-4m+1-\left(2m+5\right)^{2}=24$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2m+5\right)^{2}.

$$4m^{2}-4m+1-\left(4m^{2}+20m+25\right)=24$$

To find the opposite of 4m^{2}+20m+25, find the opposite of each term.

$$4m^{2}-4m+1-4m^{2}-20m-25=24$$

Combine 4m^{2} and -4m^{2} to get 0.

$$-4m+1-20m-25=24$$

Combine -4m and -20m to get -24m.

$$-24m+1-25=24$$

Subtract 25 from 1 to get -24.

$$-24m-24=24$$

Add 24 to both sides.

$$-24m=24+24$$

Add 24 and 24 to get 48.

$$-24m=48$$

Divide both sides by -24.

$$m=\frac{48}{-24}$$

Divide 48 by -24 to get -2.

$$m=-2$$