Question

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

Answer 1

Answer:

x = 4, 2

Step-by-step 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

$-4\times -2=8$

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

Hence, x = 4, 2