How would you factor these equations

I'm really confused, so it would be greatly appreciated if you explain. Thanks a lot! This is grade 10 math.

x^2+8x = -12

-53x+95= -5x^2-9

-6x^2+72x-312= -150

Thank you sooo much. :)

x^2+8x = -12 <-- first thing you want to do is bring the 12 to the other side of the = sign
x^2+8x +12 = 0 <--- the -12 would turn into +12 since it goes to the other side of the = sign

Now here you have to think.. of the sum and product (I'm guessing you learned that). What # multiplied by another # will give you 12 and also add up to 8.

x^2 + 8x + 12 = 0
(x + 6 )(x + 2 ) <-- I know that if I multiply 6 x 2 it gives me 12 and 6 + 2 gives me 8.

If you are not comfortable with this method you can use the quadratic formula

(-b ± √b^2 - 4ac)/2a

x^2 + 8x + 12 = 0 <-- so once you get it into this form.. you know that a = 1.. b= 8.. c = 12.. and all you do is plug into the eqn. just a side note.. a = 1 since in front of x^2 is an invisible 1 :)

(-8 ± √8^2 - 4(1)(12))/2(1)
If I solve this through I get -6,-2.. and when you write it into (x )(x ) form you know that the signs change. So I will write (x + 6)(x + 2)

Try the other two! It is the exact same and since they are larger numbers I suggest you using the quadratic formula. Just remember, -6x^2+72x-312= -150.. when you bring 150 to the other side you add it with -312.. so..

-6x^2+72x-312= -150
-6x^2+72x-312 +150 = 0
-6x^2 + 72x - 162

Good luck!

Just move everything onto the same side, and combine like terms.
You'll then have ordinary quadratic equations.

x^2+8x = -12

x^2 + 8*x + 12 = 0

(x + 2)*(x + 6) = 0

x = -2 or x = -6 <<<
################
-53x+95= -5x^2-9

5*x^2 - 53*x + 104 = 0

(5*x - 13)*(x - 8) = 0

x = 13/5 or x = 8 <<<
################
-6x^2+72x-312= -150

-6*x^2 + 72*x - 162= 0

x^2 - 12*x + 27 = 0

(x - 9)*(x - 3) = 0

x = 9 or x = 3 <<<