Solve for "x" by factoring

Question

2x(4x-5)=3

Answer 1

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

• First we have to convert the equation to 0 = ax² + bx + c
• Start by distributing 2x throughout the parentheses

2x(4x - 5) = 3

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

8x² - 10x = 3

• Then subtract 3 from both sides to make the equation equal 0

8x² - 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

Product               Sum

-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

8x² + 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 = 0

2x = 3

x = 3/2

 

4x + 1 = 0

4x = -1

x = -1/4

 

• Finally, we should check our work.

x = 3/2

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

Answer 2

Hi Jack;

2x(4x-5)=3

Let's distribute the 2x...

8x²-10x=3

Let's subtract 3 from both sides...

8x²-10x-3=3-3

8x²-10x-3=0

For the FOIL...

FIRST must be (8x)(x) or (4x)(2x).

OUTER and INNER must add-up to -10x.

LAST must be (3)(1) or (1)(3) and one number must be negative to result in the product of -3.

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

Let's FOIL...

FIRST...(4x)(2x)=8x²

OUTER...(4x)(-3)=-12x

INNER...(1)(2x)=2x

LAST...(1)(-3)=-3

8x²-12x+2x-3=0

8x²-10x-3=0

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

Either or both parenthetical equation(s) must equal zero...

4x+1=0, 4x=-1, x=-1/4

2x-3=0, 2x=3, x=3/2

Answer 3

2x(4x-5)=3

 

Expand by opening the brackets

 

8x² - 10x = 3

 

Cross 3 over to the left to become -3 and the equation equals 0

 

8x² - 10x - 3 = 0

 

Now finding the factors of the equation

 

8x² - 12x + 2x - 3 = 0

 

(8x² - 12x) + (2x - 3) = 0

 

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

 

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

 

(4x + 1) = 0

 

4x + 1 = 0

 

4x = -1

 

x = -1/4

 

or

 

(2x - 3) = 0

 

2x - 3 = 0

 

2x = 3

 

x = 3/2

 

Answer 4

2x(4x-5)=3

8x^2-10x=3

8x^2-10x-3=0

8*(-3)=-24 and -12*2=-24 and -12+2=-10

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

4x+1=0

4x=-1

x=-1/4

2x-3=0

2x=3

x=3/2

 

 

Answer 5

2x(4x-5)=3

 

8x^2-10x-3=0

 

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

 

4x + 1 = 0 or 2x - 3 = 0

 

x = -1/4 or x = 3/2