# I need to know how to set up 4w(2w+1)=2w+1 solve by factoring ?

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• First, don't follow anyone's advice if they say you should divide both sides by 2w+1. That expression might be zero and you don't want to divide by zero. In fact, if you do follow those steps, you lose one of the possible solutions.

Instead, *subtract* 2w+1 from both sides. This will get everything together on one side and leave you with a zero on the other side.

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

Now think of the second part as -1(2w + 1):

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

Then factor out the common 2w + 1:

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

The zero product rule say, if you have ab=0, then a=0 or b=0:

4w - 1 = 0

4w = 1

w = 1/4

or

2w + 1 = 0

2w = -1

w = -1/2

w = -1/2 or w = 1/4

• 4w(2w+1)=2w+1

=>

8w^2+4w=2w+1

=>

8w^2+4w-2w-1=0

=>

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

=>

(2w+1)(4W-1)=0

=>

w=-1/2 or w=1/4

• 4w(2w+1)=2w+1

8w² + 4w = 2w + 1

8w² + 2w - 1 = 0

(4x - 1)(2x + 1) = 0

4x = 1

x = 1/4

or

2x = -1

x = - 1/2

• 4w(2w+1)=2w+1

8w^2 + 4w = 2w + 1

8w^2 + 4w - 2w - 1 = 0

8w^2 + 2w - 1 = 0

(4w - 1)(2w  + 1) = 0

4w - 1 =0, 2w + 1 = 0

w = 1/4 , w = - 1/2

roots are: w = 1/4 or - 1/2... Answer//

• 4w.(2w + 1) = 2w + 1

4w.(2w + 1) = (2w + 1)

4w.(2w + 1) - (2w + 1) = 0

[4w * (2w + 1) - [1 * (2w + 1)] = 0

(4w  - 1).(2w + 1) = 0 → one of these 2 factors must be zero

First case: (4w - 1) = 0 → 4w - 1 = 0 → 4w = 1 → w = 1/4

Second case: (2w + 1) = 0 → 2w + 1 = 0 → 2w = - 1 → w = - 1/2

• For clarity... . At the level of [4w*(2w+1) - (2w+1)] = 0 you factor out  the (2w + 1) which gives (2w+1) * (4w*1 - 1) and then carry on.

• Subtract 2w+1 from both sides

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

Use the distributive property

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

Use the zero product property

4w - 1 = 0 or 2w+1 = 0

w = 1/4 or w = -1/2

• The answer is w = 1/4 and I can see it without writing it down.

Hint:  Divide both sides of the = by (2w + 1)

4w(2w+1) = 2w+1

8w² + 4w = 2w + 1

8w² + 2w – 1 = 0

(4w – 1)(2w + 1) = 0

w = 1/4, –1/2

check

4(1/4)(2(1/4)+1) = 2(1/4)+1

(2(1/4)+1) = 2(1/4)+1

ok

4(–1/2)(2(–1/2)+1) = 2(–1/2)+1

4(–1/2)(2(–1/2)+1) = 2(–1/2)+1

0 = 0

• 4w(2w + 1) = (2w + 1)

4w = (2w + 1)/(2w + 1) = 1

w = 1/4 = 0.25