2x(4x-5)=3

2x(4x - 5) = 3; Solve for x by factoring.

- First we have to convert the equation to 0 = ax
^{2}+ bx + c - Start by distributing 2x throughout the parentheses

(2x)(4x) - (2x)(5) = 3

8x

^{2}- 10x = 3- Then subtract 3 from both sides to make the equation equal 0

^{2}- 10x - 3 = 0

- Now we can factor
- To do this we must find two numbers whose product is equal to 8 times -3 and whose sum is equal to -10
- (8)(-3) = -24

-1 · 24 = -24 -1 + 24 = 23 (no)

-2 · 12 = -24 -2 + 12 = 10 (close!)

2 · -12 = -24 2 - 12 = -10 (Yes!)

- Next we need to rewrite the equation with the b term split into our two factors
- If our first try doesn't work we have to switch the two numbers

^{2}+ 2x - 12x - 3 = 0

2x(4x + 1) - 3(4x + 1) = 0

^{ }(2x - 3)(4x + 1) = 0

- It worked!
- Now we need to solve for both values of x that will make the equation equal 0

2x = 3

x = 3/2

4x + 1 = 0

4x = -1

x = -1/4

- Finally, we should check our work.

2x(4x - 5) = 3

2(3/2)(4(3/2) - 5) = 3

(6/2)(12/2 - 5) = 3

3(6 - 5) = 3

3(1) = 3

3 = 3 √

x = -1/4

2x(4x - 5) = 3

2(-1/4)(4(-1/4) - 5) = 3

(-2/4)(-4/4 - 5) = 3

-1/2(-1 - 5) = 3

-1/2(-6) = 3

6/2 = 3

3 = 3 √

**x = 3/2 and -1/4**