Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
10y3−25y2−90y
Evaluate
10y3−25y2−6y×15
Solution
10y3−25y2−90y
Show Solution
Factor the expression
5y(y+2)(2y−9)
Evaluate
10y3−25y2−6y×15
Multiply the terms
10y3−25y2−90y
Rewrite the expression
5y×2y2−5y×5y−5y×18
Factor out 5y from the expression
5y(2y2−5y−18)
Solution
More Steps
Evaluate
2y2−5y−18
Rewrite the expression
2y2+(−9+4)y−18
Calculate
2y2−9y+4y−18
Rewrite the expression
y×2y−y×9+2×2y−2×9
Factor out y from the expression
y(2y−9)+2×2y−2×9
Factor out 2 from the expression
y(2y−9)+2(2y−9)
Factor out 2y−9 from the expression
(y+2)(2y−9)
5y(y+2)(2y−9)
Show Solution
Find the roots
y1=−2,y2=0,y3=29
Alternative Form
y1=−2,y2=0,y3=4.5
Evaluate
10y3−25y2−6y×15
To find the roots of the expression,set the expression equal to 0
10y3−25y2−6y×15=0
Multiply the terms
10y3−25y2−90y=0
Factor the expression
5y(y+2)(2y−9)=0
Divide both sides
y(y+2)(2y−9)=0
Separate the equation into 3 possible cases
y=0y+2=02y−9=0
Solve the equation
More Steps
Evaluate
y+2=0
Move the constant to the right-hand side and change its sign
y=0−2
Removing 0 doesn't change the value,so remove it from the expression
y=−2
y=0y=−22y−9=0
Solve the equation
More Steps
Evaluate
2y−9=0
Move the constant to the right-hand side and change its sign
2y=0+9
Removing 0 doesn't change the value,so remove it from the expression
2y=9
Divide both sides
22y=29
Divide the numbers
y=29
y=0y=−2y=29
Solution
y1=−2,y2=0,y3=29
Alternative Form
y1=−2,y2=0,y3=4.5
Show Solution