Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(z−5)(2z+3)
Evaluate
2z2−7z−15
Rewrite the expression
2z2+(3−10)z−15
Calculate
2z2+3z−10z−15
Rewrite the expression
z×2z+z×3−5×2z−5×3
Factor out z from the expression
z(2z+3)−5×2z−5×3
Factor out −5 from the expression
z(2z+3)−5(2z+3)
Solution
(z−5)(2z+3)
Show Solution
Find the roots
z1=−23,z2=5
Alternative Form
z1=−1.5,z2=5
Evaluate
2z2−7z−15
To find the roots of the expression,set the expression equal to 0
2z2−7z−15=0
Factor the expression
More Steps
Evaluate
2z2−7z−15
Rewrite the expression
2z2+(3−10)z−15
Calculate
2z2+3z−10z−15
Rewrite the expression
z×2z+z×3−5×2z−5×3
Factor out z from the expression
z(2z+3)−5×2z−5×3
Factor out −5 from the expression
z(2z+3)−5(2z+3)
Factor out 2z+3 from the expression
(z−5)(2z+3)
(z−5)(2z+3)=0
When the product of factors equals 0,at least one factor is 0
z−5=02z+3=0
Solve the equation for z
More Steps
Evaluate
z−5=0
Move the constant to the right-hand side and change its sign
z=0+5
Removing 0 doesn't change the value,so remove it from the expression
z=5
z=52z+3=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=2−3
Divide the numbers
z=2−3
Use b−a=−ba=−ba to rewrite the fraction
z=−23
z=5z=−23
Solution
z1=−23,z2=5
Alternative Form
z1=−1.5,z2=5
Show Solution