How do you solve #(2x + 1)(x - 4) = -7#?

1 Answer
May 26, 2015

Given #color(red)((2x+1))color(blue)((x-4)) = color(orange)(-7)#

Multiply the two terms on the left side
(for demonstration purposes I used the distributive property, but there are several ways to do this)
#color(red)(2x)color(blue)((x-4)) + color(red)(1)color(blue)((x-4)) = color(orange)(-7)#

#2x^2 -8x + x -4 = color(orange)(-7)#

#2x^2-7x-4 = color(orange)(-7)#

Rearrange all non-zero terms to the left-side
#2x^2-7x+3 = 0#

Factor the left side
#(2x-1)(x-3) = 0#

State the solutions:
#x= 1/2# or #x= 3#