What are the solutions to the equation 2w(4w-1)=w(1-4w) ?

The solutions to the equation 2w(4w-1)=w(1-4w) are w=0,w= 1/4

Find the zeros of 2w(4w-1)=w(1-4w)

The zeros of 2w(4w-1)=w(1-4w) are w=0,w= 1/4

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

w = 0, w = \frac{1}{4}

Decimal Notation

w = 0, w = 0.25

Solution steps

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

Move

w (1 - 4 w)

to the left side

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

Factor

2 w (4 w - 1) - w (1 - 4 w) : 3 w (4 w - 1)

3 w (4 w - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

w = 0 or 4 w - 1 = 0

Solve

4 w - 1 = 0 : w = \frac{1}{4}

The solutions to the quadratic equation are:

w = 0, w = \frac{1}{4}

9 x^{2} - 72 = 0

6 x^{2} + 4 x + 2 = 0

(5 x - 6)^{2} = 0

m^{2} - 6 m + 13 = 0

x^{2} = 8^{2} + 8^{2}

What are the solutions to the equation 2w(4w-1)=w(1-4w) ?
The solutions to the equation 2w(4w-1)=w(1-4w) are w=0,w= 1/4
Find the zeros of 2w(4w-1)=w(1-4w)
The zeros of 2w(4w-1)=w(1-4w) are w=0,w= 1/4