What is a solution to (x-3)(x+9)=-27

-6

0

Step-by-step explanation:

By observation we can see one solution is x=0 since this will give us

(0-3)(0+9)=(-3)(9)=-27 which is the result on the right hand side.

Now this is a quadratic equation so it should have another solution. This one doesn't seem as obvious to me.

The goal normally is to get 0 on side and factor if possible or use quadratic formula.  There is also completing the square.

So I'm going to multiply (x-3)(x+9) using foil.

First: x(x)=x^2

Outer: x(9)=9x

Inner: -3(x)=-3x

Last: -3(9)=-27

Combine like terms:

x^2+6x-27

So the equation is:

x^2+6x-27=-27

Add 27 on both sides:

x^2+6x+0=0

x^2+6x=0

Factor x out:

x(x+6)=0

In order for these equation to be true one of the left hand factors need to be 0.

Let's find when x is 0, well that is when x=0.

Let's find when x+6 is 0.

x+6=0 can be solved by subtracting 6 on both sides:

x=-6

The solutions are -6 and 0.

We already checked x=0.

Let's check x=-6:

Plugging in -6 where x is in the given equation:

(-6-3)(-6+9)

(-9)(3)

-27 which is the same as right hand side.

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d