Null factor law and factoriising:

2x^2+7x=0
X(2x+7)=0
X=0 or 2x+7=0. ( the answer in the book was x=-7/2, how?

And. X^2-4=2x-4
Is it x^2-4-2x+4=o ??? If so!' how do I continue?

2x^2+7x=0

X(2x+7)=0
X=0 or 2x+7=0
ok so far

Now, if the product of two numbers (A)(B) = 0
that can only be true of one of the, or both , are equal to zero.
(try multiplying any two numbers to get a result of 0)

so either x=0 or 2x+7 = 0
x = 0 says it all
in
2x+7 = 0
2x = -7 , (simple equation rule)
x = -7/2 , (simple equation rule)

your second question:

x^2 - 2x = 0 , after you take everything to the left
x(x-2) = 0
same as above and even simpler.

2 x ^ 2 + 7 x = 0

x ( 2 x + 7 ) = 0

Obviously solution x = 0

2 x + 7 = 0 Subtract 7 to both sides

2 x + 7 - 7 = 0 - 7

2 x = - 7 Divide both sides by 2

x = - 7 / 2

Solutions x = 0 and x = - 7 / 2

x ^ 2 - 4 = 2 x - 4 Add 4 to both sides

x ^ 2 - 4 + 4 = 2 x - 4 + 4

x ^ 2 = 2 x Subtract 2 x to both sides

x ^ 2 - 2 x = 2 x - 2 x

x ^ 2 - 2 x = 0

x ( x - 2 ) = 0

Obviously solution x = 0

x - 2 = 0 Add 2 to both sides

x - 2 + 2 = 0 + 2

x = 2

Solutions x = 0 and x = 2

To solve the equation 2x^2 + 7x = 0, we can use the null factor law. The null factor law states that if the product of two factors is equal to zero, then at least one of the factors must be zero. In this case, we have:

2x^2 + 7x = 0

To find the factors, we can rearrange the equation:

x(2x + 7) = 0

Now we have a product of two factors, which are x and (2x + 7). According to the null factor law, at least one of these factors must be zero. So we set each factor to zero and solve for x:

x = 0 or 2x + 7 = 0

For the second equation, 2x + 7 = 0, we can solve for x as follows:

2x + 7 = 0
2x = -7
x = -7/2

So the solutions to the equation 2x^2 + 7x = 0 are x = 0 and x = -7/2.

Regarding the equation x^2 - 4 = 2x - 4, you made a slight error in your attempt to rearrange it. The correct rearrangement would be:

x^2 - 2x = 0

To continue solving this equation, we can again use the null factor law:

x(x - 2) = 0

Setting each factor to zero, we have:

x = 0 or x - 2 = 0

Solving the second equation, x - 2 = 0, we get:

x = 2

So the solutions to the equation x^2 - 4 = 2x - 4 are x = 0 and x = 2.