Question
Simplify the expression
6x3−60x2+150x
Evaluate
3(x−5)×2(x−5)x
Multiply the terms
6(x−5)(x−5)x
Multiply the terms
6x(x−5)(x−5)
Multiply the terms
6x(x−5)2
Expand the expression
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Evaluate
(x−5)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×5+52
Calculate
x2−10x+25
6x(x2−10x+25)
Apply the distributive property
6x×x2−6x×10x+6x×25
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
6x3−6x×10x+6x×25
Multiply the terms
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Evaluate
6x×10x
Multiply the numbers
60x×x
Multiply the terms
60x2
6x3−60x2+6x×25
Solution
6x3−60x2+150x
Show Solution

Find the roots
x1=0,x2=5
Evaluate
3(x−5)×2(x−5)x
To find the roots of the expression,set the expression equal to 0
3(x−5)×2(x−5)x=0
Multiply the terms
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Multiply the terms
3(x−5)×2(x−5)x
Multiply the terms
6(x−5)(x−5)x
Multiply the terms
6x(x−5)(x−5)
Multiply the terms
6x(x−5)2
6x(x−5)2=0
Elimination the left coefficient
x(x−5)2=0
Separate the equation into 2 possible cases
x=0(x−5)2=0
Solve the equation
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Evaluate
(x−5)2=0
The only way a power can be 0 is when the base equals 0
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=0x=5
Solution
x1=0,x2=5
Show Solution
