How do you solve (2x + 1)(x - 4) = -7(2x+1)(x4)=7?

1 Answer
May 26, 2015

Given color(red)((2x+1))color(blue)((x-4)) = color(orange)(-7)(2x+1)(x4)=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(x4)+1(x4)=7

2x^2 -8x + x -4 = color(orange)(-7)2x28x+x4=7

2x^2-7x-4 = color(orange)(-7)2x27x4=7

Rearrange all non-zero terms to the left-side
2x^2-7x+3 = 02x27x+3=0

Factor the left side
(2x-1)(x-3) = 0(2x1)(x3)=0

State the solutions:
x= 1/2x=12 or x= 3x=3