Question
Factor the expression
(2x−5)(2x+1)
Evaluate
4x2−8x−5
Rewrite the expression
4x2+(2−10)x−5
Calculate
4x2+2x−10x−5
Rewrite the expression
2x×2x+2x−5×2x−5
Factor out 2x from the expression
2x(2x+1)−5×2x−5
Factor out −5 from the expression
2x(2x+1)−5(2x+1)
Solution
(2x−5)(2x+1)
Show Solution

Find the roots
x1=−21,x2=25
Alternative Form
x1=−0.5,x2=2.5
Evaluate
4x2−8x−5
To find the roots of the expression,set the expression equal to 0
4x2−8x−5=0
Factor the expression
More Steps

Evaluate
4x2−8x−5
Rewrite the expression
4x2+(2−10)x−5
Calculate
4x2+2x−10x−5
Rewrite the expression
2x×2x+2x−5×2x−5
Factor out 2x from the expression
2x(2x+1)−5×2x−5
Factor out −5 from the expression
2x(2x+1)−5(2x+1)
Factor out 2x+1 from the expression
(2x−5)(2x+1)
(2x−5)(2x+1)=0
When the product of factors equals 0,at least one factor is 0
2x−5=02x+1=0
Solve the equation for x
More Steps

Evaluate
2x−5=0
Move the constant to the right-hand side and change its sign
2x=0+5
Removing 0 doesn't change the value,so remove it from the expression
2x=5
Divide both sides
22x=25
Divide the numbers
x=25
x=252x+1=0
Solve the equation for x
More Steps

Evaluate
2x+1=0
Move the constant to the right-hand side and change its sign
2x=0−1
Removing 0 doesn't change the value,so remove it from the expression
2x=−1
Divide both sides
22x=2−1
Divide the numbers
x=2−1
Use b−a=−ba=−ba to rewrite the fraction
x=−21
x=25x=−21
Solution
x1=−21,x2=25
Alternative Form
x1=−0.5,x2=2.5
Show Solution
