Solve by factoring x^2 plus 8x ,minus 20 equal 0

x^2 + 8x - 20 = 0

(x + 10) (x-2) = 0

x = -10, 2

All terms must be multiplied for factoring.

x^2 + 8x - 20 = 0
Start by putting an x as the front of each term.

(x _)(x _) = 0
When FOILing, we know that the "last" has to be a -20, so one sign is negative, and the other is positive.

(x + _)(x - _) = 0
When multiplied, the two blanks have to equal -20. We could have 20 and 1, 10 and 2, 5 and 4 (with one of the numbers being negative.)

Well, one of the negatives plus the positive has to equal 8... so 10 and 2 are what we want.

(x + 2)(x - 10) = 0
Check by foiling.

x^2 - 10x + 2x - 20 = 0
x^2 - 8x - 20 = 0

That's not our original expression, so the signs need to be switched.

(x - 2)(x + 10) = 0
Check again.

x^2 + 10x - 2x - 20 = 0
x^2 + 8x - 20 = 0

That's what we want, so (x-2)(x+10) is the answer.

Oh, and to solve, set each term equal to 0.

x - 2 = 0, x + 10 = 0
x = 2, x = -10

To solve the equation x^2 + 8x - 20 = 0 by factoring, we need to find two numbers whose product is equal to -20 (the coefficient of the constant term) and whose sum is equal to 8 (the coefficient of the linear term).

Let's try to identify the factors of -20:
-20 = (-1) * (20) = (-2) * (10) = (-4) * (5) = (1) * (-20) = (2) * (-10) = (4) * (-5)

Now, we need to find the pair of factors that can be combined to give the coefficient of the linear term, which is positive 8. Looking at the factors, we can see that (-2) and (10) satisfy this condition.

So we can now write the equation as:
(x - 2)(x + 10) = 0

To get the solutions, we set each factor equal to zero:
x - 2 = 0 or x + 10 = 0

Solving each equation for x, we get:
x = 2 or x = -10

Therefore, the solutions to the equation x^2 + 8x - 20 = 0 are x = 2 and x = -10.