Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
−(n−25)(n−16)
Evaluate
41n−n2−400
Reorder the terms
−n2+41n−400
Rewrite the expression
−n2+(16+25)n−400
Calculate
−n2+16n+25n−400
Rewrite the expression
−n×n+n×16+25n−25×16
Factor out −n from the expression
−n(n−16)+25n−25×16
Factor out 25 from the expression
−n(n−16)+25(n−16)
Factor out n−16 from the expression
(−n+25)(n−16)
Solution
−(n−25)(n−16)
Show Solution
Find the roots
n1=16,n2=25
Evaluate
41n−n2−400
To find the roots of the expression,set the expression equal to 0
41n−n2−400=0
Factor the expression
More Steps
Evaluate
41n−n2−400
Reorder the terms
−n2+41n−400
Rewrite the expression
−n2+(16+25)n−400
Calculate
−n2+16n+25n−400
Rewrite the expression
−n×n+n×16+25n−25×16
Factor out −n from the expression
−n(n−16)+25n−25×16
Factor out 25 from the expression
−n(n−16)+25(n−16)
Factor out n−16 from the expression
(−n+25)(n−16)
(−n+25)(n−16)=0
When the product of factors equals 0,at least one factor is 0
−n+25=0n−16=0
Solve the equation for n
More Steps
Evaluate
−n+25=0
Move the constant to the right-hand side and change its sign
−n=0−25
Removing 0 doesn't change the value,so remove it from the expression
−n=−25
Change the signs on both sides of the equation
n=25
n=25n−16=0
Solve the equation for n
More Steps
Evaluate
n−16=0
Move the constant to the right-hand side and change its sign
n=0+16
Removing 0 doesn't change the value,so remove it from the expression
n=16
n=25n=16
Solution
n1=16,n2=25
Show Solution