Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(2z−3)(2z+1)
Evaluate
4z2−4z−3
Rewrite the expression
4z2+(2−6)z−3
Calculate
4z2+2z−6z−3
Rewrite the expression
2z×2z+2z−3×2z−3
Factor out 2z from the expression
2z(2z+1)−3×2z−3
Factor out −3 from the expression
2z(2z+1)−3(2z+1)
Solution
(2z−3)(2z+1)
Show Solution
Find the roots
z1=−21,z2=23
Alternative Form
z1=−0.5,z2=1.5
Evaluate
4z2−4z−3
To find the roots of the expression,set the expression equal to 0
4z2−4z−3=0
Factor the expression
More Steps
Evaluate
4z2−4z−3
Rewrite the expression
4z2+(2−6)z−3
Calculate
4z2+2z−6z−3
Rewrite the expression
2z×2z+2z−3×2z−3
Factor out 2z from the expression
2z(2z+1)−3×2z−3
Factor out −3 from the expression
2z(2z+1)−3(2z+1)
Factor out 2z+1 from the expression
(2z−3)(2z+1)
(2z−3)(2z+1)=0
When the product of factors equals 0,at least one factor is 0
2z−3=02z+1=0
Solve the equation for z
More Steps
Evaluate
2z−3=0
Move the constant to the right-hand side and change its sign
2z=0+3
Removing 0 doesn't change the value,so remove it from the expression
2z=3
Divide both sides
22z=23
Divide the numbers
z=23
z=232z+1=0
Solve the equation for z
More Steps
Evaluate
2z+1=0
Move the constant to the right-hand side and change its sign
2z=0−1
Removing 0 doesn't change the value,so remove it from the expression
2z=−1
Divide both sides
22z=2−1
Divide the numbers
z=2−1
Use b−a=−ba=−ba to rewrite the fraction
z=−21
z=23z=−21
Solution
z1=−21,z2=23
Alternative Form
z1=−0.5,z2=1.5
Show Solution