Math Help How do I work this problem out step by step?

How do I work out a problem such as this one:








( 2 z - 1 ) ( 2 - z ) = 0Math Help How do I work this problem out step by step?
First, take the equation apart. Basically, you have one number multiplied by another number that equals zero. So, this means that at least one of the numbers must equal 0 in order so this equation to be true.





That means we need to figure out what number ';z'; is that would cause either (2z-1) or (2-z) to = 0.





First: When does 2z - 1 = 0?


2z - 1 = 0


2z = 1


z = 1/2





2z - 1 = 0 when z = 1/2





Second: When does 2-z = 0 ?


2 - z = 0


2 = 2





2 - z = 0 when z = 2.





So that means, in order for (2z-1)(2-z) = 0, z must be equal to 1/2 or 2.





z = 1/2, 2Math Help How do I work this problem out step by step?
Well for these questions, u have to remember the smile face rule.


(a + b)(c + d) = ac + bd + ad+ bc





(2z - 1)(2 - z) = 0


2z x 2 -1 x -z + 2z x -z + -1 x 2


4z + z - 2z^2 - 2


-2z^2 + 5z - 2 = 0





Using the quadratic formula x = -b +\- Square Root (b^2 - 4ac) / 2a





we find z to be 0.5 and 2
multiply 2z x 2, 2z x -z, -1 x 2, and -1 x -z.... with those numbers, you do all the math goodness of subtracting/adding/dividing from each side and find the answer!





i dont know if that was specific enough



(a + b)(c + d) = ac + bd + ad+ bc





(2z - 1)(2 - z) = 0


2z x 2 -1 x -z + 2z x z + -1 x 2


4z + z + 2z^2 - 2


2z^2 + 5z - 2 = 0





quadratic formula x = -b + and - Square Root (b^2 - 4ac) / 2a





find z which is 0.35 and -2.85
well you just take each bracket it solve it





2z-1 = 0


z = 1/2





2-z = 0


z = 2





therefore your two roots are z = 1/2 or z = 2