Help Factorising this equation

I'm learning maths from home, and i'm working through factorisation. i've been given the answer but i'm unsure on the workings, please can someone explain?

The equation i'm stuck with has been transposed from:

6x^2 = 5 -13x

to

6x^2 +13x -5 = 0

I'm then asked to factorise the left hand side and the answer is (3x -1) (2x+5) = 0

I would normally approach the equation by finding factors of "-5" that add up to "+13" but doesn't appear to be the correct route.


Any help would be greatly appreciated!

When the coefficient of x^2 isn't 1, you would use the method of grouping.
Multiply the constant -5 and leading coefficient 6.
-30
Find factors of -30 that add up to +13. Those are +15 and -2. Write the x coefficient as the sum of these.
6x^2 + (15 - 2)x - 5 = 0
Separate the terms.
6x^2 + 15x - 2x - 5 = 0
Factor, or group, the first two terms, and the second two terms.
3x(2x + 5) - 1(2x + 5)
Use the reverse rule of distribution.
a(c + d) + b(c + d) = (a + b)(c + d)

3x(2x + 5) - 1(2x + 5) = (3x - 1)(2x + 5)

That is the way to factor by grouping.

You are correct so far as you go!!!!
However, write down all the factors of '6'

6 x 1 = 6
3 x 2 = 6
And the factors of '5'

5 x 1 = 5
You must select a pair of factors from '6' and the pair from '5' ,which when multiplied together and then added/subtracted , equal '13'

Hence
3 x 5 = 15 & 2 x 1 = 2
15 - 2 = 13 The required result.
Putting into brackets
Note that the pairs of multiples go into opposite brackets.

(3x 1)(2x 5) = 0

Next to put in the correct signs. Note the the constant '5' is negative. This means that the two signs are different.
The term '13x' is positive so the larger multiple is positive.