help me solve (2x-1)(3x+7)=0?

This is just how I do it

It's already in factorised form so you don't need to change it
(2x-1)(3x+7)=0

Using the Null Factor Law that anything multiplied by zero equals zero.

For (2x-1) ask yourself what you would substitute for x to make it zero. Since it's 2x, divide -1 by two so it becomes x -1/2. -1/2+1/2 =0. So one of the values of x is 1/2. You could leave it as a fraction or make it 0.5.

For (3x+7) ask yourself what you would substitute for x to make it zero. Since it's 3x, divide 7 by three so it becomes x +7/3. 7/3 -7/3 =0. So the other value of x is -7/3. It's a reacurring number so it's probably best to leave it as a fraction.

For this one you should probably leave both answers as a fraction.

So x = 1/2 or -7/3

Hope this helps.

(2x - 1) (3x + 7) = 0
2x - 1 = 0 OR 3x + 7 = 0
x = 1/2 , x = - 7/3

First 2x-1=0, so
2x=1,
x=1/2.

And 3x+7=0
3x=-7
x=-7/3.

So, x=1/2 and x=-7/3.

2x-1=0
2x=1
x=1/2
3x+7=0
3x=-7
x=-7/3
x=1/2 or -7/3

(2x - 1)(3x + 7) = 0

2x - 1 = 0
2x = 1
x = 1/2 (0.5)

3x + 7 = 0
3x = -7
x = -7/3

∴ x = -7/3 , 1/2 (0.5)

You need to find each separately so:
2x-1= 0
You solve it like an equation
2x=1
x=1/2 (half/0.5)

Then you do the next one:
3x+7=0
3x=-7
x=-7/3

So x={1/2, -7/3}

i) (2x - 1) = 0

ii) (3x + 7) = 0

i) 2x = 1

x = 1/2

ii) 3x = -7

x = -7/3

ANS = {1/2, -7/3}

(2x - 1) (3x + 7) = 0


2x - 1 = 0
2x = 1
x = 1/2

3x + 7 = 0
3x = -7
x = - 7/3

So, the answer for x ( -7/3 , 1/2 )

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Reference:
(ax+b) (ax-b) = 0

ax+b = 0 / (ax-b)

Because zero divided by --whatever-- is still zero.
Then we have it as,

ax+b = 0.

Then it works the same with (ax - b) = 0. it's from

(ax-b) = 0 / (ax+b)

If three factor appears
(ax+b)(ax+c)(ax+d) = 0, we have 3 values for x.

And the same with 4 factor above. But under condition, the formula must always equals to = 0 (zero).

Do not ever try to factor any other variable/numbers except to be valued by this one, "= 0".

All variables in left = 0,
or
0 = all variables in right.

Note:
The + or - in the factor is just for an example.

set each part equal to zero

2x-1 = 0
3x+7 = 0
and solve for x