Explanation:

x2+4x-12=0

Two solutions were FOUND :

x = 2

x = -6

Reformatting the INPUT :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

Step 1 :

Trying to factor by splitting the MIDDLE term

1.1 Factoring x2+4x-12

The first term is, x2 its coefficient is 1 .

The middle term is, +4x its coefficient is 4 .

The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum EQUALS the coefficient of the middle term, which is 4 .

-12 + 1 = -11

-6 + 2 = -4

-4 + 3 = -1

-3 + 4 = 1

-2 + 6 = 4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 6

x2 - 2x + 6x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-2)

Add up the last 2 terms, pulling out common factors :

6 • (x-2)

Step-5 : Add up the four terms of step 4 :

(x+6) • (x-2)

Which is the desired factorization

Equation at the END of step 1 :

(x + 6) • (x - 2) = 0

Step 2 :

Theory - Roots of a product :

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.