help me math stars?

Question

how to work out this problem by zero factor property
2w(4w+1)=1

Answer 1

Start with distributing the 2w.
2w(4w + 1)=1
2w*4w + 2w*1 = 1
8w^2 + 2w = 1
8w^2 + 2w - 1 = 1 - 1
8w^2 + 2w - 1 = 0
~Now factor~
(2w + 1)(4w - 1) = 0

~Check: (2w + 1)(4w - 1) = 2w*4w - 2w*1 + 1*4w - 1 = 8w^2 - 2w + 4w - 1 = 8w^2 + 2x - 1 ~
~Since one of the expressions in ONE of the parentheses needs to equal 0 to have the whole equation equal 0. We can have both equal 0~

(2w + 1)(4w - 1) = 0
2w + 1 = 0 OR 4w - 1 = 0
2w + 1 - 1 = 0 - 1 OR 4w - 1 + 1 = 0 + 1
2w/2 = -1/2 OR 4w/4 = 1/4
w = -1/2 OR w = 1/4

So your answer is (using zero factor property) :
w = {-1/2 , 1/4}

Answer 2

Rewrite to give a zero result on the right: 8w^2 + 2w - 1 = 0. Now try to factor it: (2w+1)(4w-1) = 0. At least one of the factors must equal zero in order for the product to be zero. So either 2w+1 = 0, in which case 2w = -1 and w = -1/2, OR/AND 4w-1 = 0, in which case 4w = 1 and w = 1/4. The two "roots" of the equation are (-1/2, +1/4)