Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
3(r+2)(r+5)
Evaluate
3r2+21r+30
Rewrite the expression
3r2+3×7r+3×10
Factor out 3 from the expression
3(r2+7r+10)
Solution
More Steps
Evaluate
r2+7r+10
Rewrite the expression
r2+(5+2)r+10
Calculate
r2+5r+2r+10
Rewrite the expression
r×r+r×5+2r+2×5
Factor out r from the expression
r(r+5)+2r+2×5
Factor out 2 from the expression
r(r+5)+2(r+5)
Factor out r+5 from the expression
(r+2)(r+5)
3(r+2)(r+5)
Show Solution
Find the roots
r1=−5,r2=−2
Evaluate
3r2+21r+30
To find the roots of the expression,set the expression equal to 0
3r2+21r+30=0
Factor the expression
More Steps
Evaluate
3r2+21r+30
Rewrite the expression
3r2+3×7r+3×10
Factor out 3 from the expression
3(r2+7r+10)
Factor the expression
More Steps
Evaluate
r2+7r+10
Rewrite the expression
r2+(5+2)r+10
Calculate
r2+5r+2r+10
Rewrite the expression
r×r+r×5+2r+2×5
Factor out r from the expression
r(r+5)+2r+2×5
Factor out 2 from the expression
r(r+5)+2(r+5)
Factor out r+5 from the expression
(r+2)(r+5)
3(r+2)(r+5)
3(r+2)(r+5)=0
Divide the terms
(r+2)(r+5)=0
When the product of factors equals 0,at least one factor is 0
r+2=0r+5=0
Solve the equation for r
More Steps
Evaluate
r+2=0
Move the constant to the right-hand side and change its sign
r=0−2
Removing 0 doesn't change the value,so remove it from the expression
r=−2
r=−2r+5=0
Solve the equation for r
More Steps
Evaluate
r+5=0
Move the constant to the right-hand side and change its sign
r=0−5
Removing 0 doesn't change the value,so remove it from the expression
r=−5
r=−2r=−5
Solution
r1=−5,r2=−2
Show Solution