Question

Use factoring to solve the equation for x: (x−2)(2x−3)=(x−2)(x+1).

Answer 1

x = 4, 2

Explanation:

`(x-2)(2x-3)=(x-2)(x+1)`

`\\\Rightarrow 2x^2-7x+6=x^2+x-2x-2\\\Rightarrow 2x^2-7x+6-x^2+x-2x-2=0\\\Rightarrow x^2-6x+8=0`

While splitting the middle term the sum of the term should give us the middle term and their product should give the last term

`\\\Rightarrow x^2-4x-2x+8=0`

-4-2 = -6

`-4* -2=8`

`\\\Rightarrow (x-4)(x-2)=0\\\Rightarrow x=4, 2`

Hence, x = 4, 2