48=b2-2b

Rewrite the equation as b2-2b=48.

b2-2b=48

Move 48 to the left side of the equation by subtracting it from both sides.

b2-2b-48=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -48 and whose sum is -2.

-8,6

Write the factored form using these integers.

(b-8)(b+6)=0

(b-8)(b+6)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

b-8=0

b+6=0

Set the first factor equal to 0.

b-8=0

Add 8 to both sides of the equation.

b=8

b=8

Set the next factor equal to 0.

b+6=0

Subtract 6 from both sides of the equation.

b=-6

b=-6

The final solution is all the values that make (b-8)(b+6)=0 true.

b=8,-6

Solve for b 48=b^2-2b