Factorising Help Needed?

Put all the variables on the left side for both equations:
a) -6x^2 -x +7 =0
Multiply through by -1:
6x^2 +x -7=0
(6x +7)(x-1) =0 from trial and error
x=-7/6, x=1

b) 6x^2 -11x=0
x(6x-11)=0
x=0, x= 11/6

a)
5x^2 - 10x^2 = -7 + x + x^2
-5x^2 - x^2 - x + 7 = 0
-6x^2 - x + 7 = 0
6x^2 + x - 7 = 0
6x^2 + 7x - 6x - 7 = 0
(6x^2 + 7x) - (6x + 7) = 0
x(6x + 7) - 1(6x + 7) = 0
(6x + 7)(x - 1) = 0

6x + 7 = 0
6x = -7
x = -7/6

x - 1 = 0
x = 1

∴ x = -7/6 , 1

= = = = = = = =

b)
4x^2 + 17x = 6x - 2x^2
4x^2 + 2x^2 + 17x - 6x = 0
6x^2 + 11x = 0
x(6x + 11) = 0

x = 0

6x + 11 = 0
6x = -11
x = -11/6

∴ x = -11/6 , 0

take out the biggest element you may from each and each variety, this is in each and every variety from the equation, so for the 1st you may take out 4, which provides you with 4(x+2), through fact 4 situations x is 4x and four situations 2 is 8. Do the comparable for something.

Part a)
- 6x² - x + 7 = 0
6x² + x - 7 = 0
(6x + 7)(x - 1) = 0
x = 7/6 , x = 1

Part b)
6x² + 11x = 0
x (6x + 11) = 0
x = 0 , x = - 11/6

a) 5x² - 10x² = -7 + x + x²
collect terms
0 = -7 + x + 6x²
(6 x +7)( x -1) = 0
x = 1, x = -7/6

b) 4x² + 17x = 6x – 2x²
2 x²+11 x = 0
x( 2x +11) = 0
x = 0, x = -11/2

1- get all the terms in one side

5x² - 10x² + 7- x - x²=0

-6x² - x+ 7=0

multiply by-1

6x²+x -7=0

( x - 1)( 6x+ 7 )=0 >>> x=1 x=-7/6

you choose those as if you re multiply them again you will have the equation again

hint : consider the second order term and the absolute term, try to get two factors of each of them that if you multiply them and add then=m you will get the first order term
in that example 6x²=6x *x
-7= -1 * 7

and so (6x*-1) + (7*x)=x

2.
4x² + 17x = 6x – 2x²
4x² + 17x - 6x + 2x²=0
6x² +11x=0

actually this is easier than much one because the abs. term is zero,
so you can get x as a common factor of the terms.
x( 6x+11)=0 >>>>> x=0 x=-11 / 6