Question

x(x+1)+(x+2)(x+3)=42

Answer 1

Given, x(x+1) + (x+2)(x+3) = 42 can be written as,

           x(x+1) + (x+2)(x+3) - 42 = 0

           x^2 + x + x^2 + 3x + 2x + 6 - 42 = 0

           2x^2 + 6x - 36 = 0

           2(x^2 + 3x - 18) = 0

           2(x+6)(x-3) = 0

             x = -6, 3.


Hope this helps!

Answer 2

x^2+x+x^2+5x+6=42
2x^2+6x+6=42
divide both sides by 2
x^2+3x+3=21
x^2+3x-18=0
x^2+6x-3x-18
x(x+6)-3(x+6)
(x+6)(x-3)
x-3=0
x=3
x+6=0
x=-6