2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation
step-by-step explanation:
equation
you are asked to write the equation
expression = 0
using the given expression. when you do that, you have
2x^2-2x-12 = 0
factoring
you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.
2(x^2 -x -6) = 0
if you multiply the binomials (x+a)(x+b), you get
(x +a)(x +b) = x^2 +(a+b)x +ab
this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.
-6 = -1×6 = -2×3 = -3×2 = -6×1
the factor pair that sums to -1 is {-3, 2}, so our factorization is
2(x -3)(x +2) = 0
solutions
the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means
x - 3 = 0
x = 3 . . . add 3 to both sides of the equation
or
x +2 = 0
x = -2 . . . add -2 to both sides of the equation
the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.
