Answer
$x=${$1,\dfrac{5 }{2}$}
Work Step by Step
Given: $(2x-6)(x+2)(=5(x-1)-12$
Re-write the given equation as: $2x^2+4x-6x-12=5x-5-12$
This implies that $2x^2-7x+5=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(2)(5)}}{2(2)}$
or, $x=\dfrac{7 \pm \sqrt {9}}{4}$
or, $x=${$\dfrac{7 - 3}{4},\dfrac{7+3}{4}$}
Hence, our solution set is: $x=${$1,\dfrac{5 }{2}$}
