Algebra

+x+=+
-x-=+

-x+=-
+x-=-

(X+4)(X+3) firstly, times the first X by the second X.
Then times the first X by the second number.
Thirdly, times the first number by the X and then the second number.

This will give you the answer as;

X(to the power of 2) + 3X + 4X + 12

Then, simpify is as; X(to the power of 2) + 7X + 12

Look for a pair of numbers that add to make the middle number and times to make the last number... e,g:

X(to the power of 2) + 8X + 7

Adds to make: 8
Times to get: 7
= 1 and 7

(X+1)(X+7)

You can do this without a calculator.

1. Multiply the coefficient and the end.
2. Break the middle term.
3. Factorise twice.
4. Create new brackets.
5. Solve.

4X(to the power of 2) - 6X - 18 = 0
Adds to make: 6
Times to get: 72
= -12 and 6

4X(to the power of 2) - 12X + 6X - 18
4X(x-3) + 6X(X-3)
If two brackets are equal, you've done it correctly.
(X-3)(4X+6)

X=3 or 6/4 = 15