Math Geniuses-- Solve (x-5)(x+3) and show work.?

Values of x:
x - 5 = 0, x = 5
x + 3 = 0, x = - 3

Answer: x = 5, - 3

Simplify the factors to prove values of x:
= (x - 5)(x + 3)
= x² + 3x - 5x - 15
= x² - 2x - 15 OR x² - 2x = 15

Proof (x = 5):
5² - 2(5) = 15
25 - 10 = 15
15 = 15

Proof (x = - 3):
(- 3)² - 2(- 3) = 15
9 + 6 = 15
15 = 15

Assuming 0 =(x-5)(x+3) then

Using the null factor law, one of the brackets have to be zero, so
(x-5)=0 or (x+3)=0

so x = 5 or x = -3.

Solve:

(x - 5)(x + 3)

Multiply using the FOIL Method

x * x = x^2

x * 3 = 3x

-5 * x = -5x

-5 * 3 = -15

x^2 + 3x - 5x - 15

Combine like terms:

3x - 5x = -2x

x^2 - 2x - 15

Subproblem 1

x - 5 = 0

Add 5 to each side of the equation

x - 5 + 5 = 0 + 5

x = 5

Subproblem 2

x + 3 = 0

Add -3 to each side of the equation

x + 3 - 3 = 0 - 3

x = -3

Solution:

x = 5, -3

There is nothing to solve for here. This is just an expression, not an equation. Use the FOIL method. Check out my Math Variety blog posts about the FOIL method for an explanation of what it is, practice problems, and solutions. http://mathvariety.blogspot.com/2009/04/foil-method.html
http://mathvariety.blogspot.com/2009/05/foil-method-practice-problems.html
http://mathvariety.blogspot.com/2009/05/foil-method-solutions-to-practice.html

F: x*x=x^2
O: x*3=3x
I: -5*x= -5x
L: -5*3= -15

This all adds to x^2-2x-15 (answer).

if equal 0,
then x=5 & x=-3

If the equation is 0 = (x - 5)(x + 3), then use the Zero Product Property.

0 = x - 5
x = 5

0 = x + 3
x = -3

5 , -3

What do you mean by "solve" (x-5)(x+3)? It is not an equation.

Some things you could mean and how to solve:

* Solve for x= some number -- replace all the x's with that number and do the arithmetic

* Find the roots of (x-5)(x+3) = 0 -- The roots here are just the x value(s) when y is zero. Googol explains this and it is pretty straightforward. If either (x-5) or (x+3) is zero, the product is zero so x is 5 or -3

* Multiply the two factors to get the equivalent expression as a sum of factors of x raised to a power (ax^2 + bx^1 + cx^0). Use the distributive property to get x^2 -2x -15

0=(x-5)(x+3) this means that 0=x-5 and 0=x+3

solve
0=x-5
x=5

0=x+3
x=-3

Expand.
(x - 5)(x + 3)
= x*x + x*3 - 5*x - 5*3
= x^2 + 3x - 5x - 15
= x^2 - 2x - 15

If you're just trying to factor it, it would be x^2 -2x-15 by using the FOIL rules (First, outer, inner, last) meaning you multiply x and x, then x and -5, then x and 3, then -5 and 3. You would end up with x^2 -(-5x)+3x-15, then add the common ones.