I Need Help On This Factorise And Solve Question

I need help on these. i can't understand how to do them, can someone show me how do these.
x2 - 2x -15 = 0

AND

Solve
3x2 - 12 = 0

AND

Show that the equation (2x-1)2 + 9 - 6x2 can be simplified to
5x2 - 2x - 4 = 0

x^2 - 2x - 15 = 0

We notice that -2 = 3 - 5 and that -15 = 3 * -5, hence:

(x + 3)(x - 5) = 0

---

3x^2 - 12 = 0

We divide both sides by 3 as all coefficients on the left-hand side are multiples of 3:

x^2 - 4 = 0

We add 4 to both sides:

x^2 = 4

We take the square root of both sides and get:

x = √4 = ±2

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(2x - 1)^2 + 9 - 6x^2 = 0

Expand the brackets:

4x^2 - 4x + 1 + 9 - 6x^2 = 0

Combine the like terms:

-2x^2 - 4x + 10 = 0

Unless you wrote something down incorrectly, the third problem is incorrect, unless I am misunderstanding you.

To factorize the first one, consider its form:

ax^2+bx+c=0

Where, 1x^2-2x-15=0
a=1 b=-2 c=-15

You need to find two numbers that multipy to give ac and add to give -2.

it will be in the form, (x+?)(x+?)=0

The second one you just need to make x the subject,

add 12 to both sides, 3x^2=12
divide 3 from both sides, x^2=4
square root both sides, x=+-2
Remember a square root can be positive or negative.

x2 - 2x -15 = 0 or
x^2 -5x +3x -15 = 0 or
x(x-5) + 3(x-5) = 0 or
(x-5)(x+3) or x = 5 or -3

AND

Solve
3x2 - 12 = 0 or x^2 -4 = 0 or (x+2)(x-2) = 0 or
x = -2 or 2

AND
(2x-1)2 + 9 - 6x2 = 0 or
4x^2 -4x +1 + 9 -6x^2 = 0 or
-2x^2 -4x + 10 = 0
2x^2 +2x -5 = 0 and not
5x2 - 2x - 4 = 0
Given question is wrong!

i know the reason why