Solve -left(2m-3right)^2+2mleft(2m-3right)+m-3=3

$$- { \left(2m-3 \right) }^{ 2 } +2m \left( 2m-3 \right) +m-3 = 3$$

Solve for m

$$m = \frac{15}{7} = 2\frac{1}{7} \approx 2.142857143$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-3\right)^{2}.

$$-\left(4m^{2}-12m+9\right)+2m\left(2m-3\right)+m-3=3$$

To find the opposite of 4m^{2}-12m+9, find the opposite of each term.

$$-4m^{2}+12m-9+2m\left(2m-3\right)+m-3=3$$

Use the distributive property to multiply 2m by 2m-3.

$$-4m^{2}+12m-9+4m^{2}-6m+m-3=3$$

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

$$12m-9-6m+m-3=3$$

Combine 12m and -6m to get 6m.

$$6m-9+m-3=3$$

Combine 6m and m to get 7m.

$$7m-9-3=3$$

Subtract 3 from -9 to get -12.

$$7m-12=3$$

Add 12 to both sides.

$$7m=3+12$$

Add 3 and 12 to get 15.

$$7m=15$$

Divide both sides by 7.

$$m=\frac{15}{7}$$