Question
Simplify the expression
−25n3−6
Evaluate
5n3−10n2×3n−6
Multiply
More Steps

Multiply the terms
−10n2×3n
Multiply the terms
−30n2×n
Multiply the terms with the same base by adding their exponents
−30n2+1
Add the numbers
−30n3
5n3−30n3−6
Solution
More Steps

Evaluate
5n3−30n3
Collect like terms by calculating the sum or difference of their coefficients
(5−30)n3
Subtract the numbers
−25n3
−25n3−6
Show Solution

Find the roots
n=−5330
Alternative Form
n≈−0.621447
Evaluate
5n3−10n2×3n−6
To find the roots of the expression,set the expression equal to 0
5n3−10n2×3n−6=0
Multiply
More Steps

Multiply the terms
10n2×3n
Multiply the terms
30n2×n
Multiply the terms with the same base by adding their exponents
30n2+1
Add the numbers
30n3
5n3−30n3−6=0
Subtract the terms
More Steps

Simplify
5n3−30n3
Collect like terms by calculating the sum or difference of their coefficients
(5−30)n3
Subtract the numbers
−25n3
−25n3−6=0
Move the constant to the right-hand side and change its sign
−25n3=0+6
Removing 0 doesn't change the value,so remove it from the expression
−25n3=6
Change the signs on both sides of the equation
25n3=−6
Divide both sides
2525n3=25−6
Divide the numbers
n3=25−6
Use b−a=−ba=−ba to rewrite the fraction
n3=−256
Take the 3-th root on both sides of the equation
3n3=3−256
Calculate
n=3−256
Solution
More Steps

Evaluate
3−256
An odd root of a negative radicand is always a negative
−3256
To take a root of a fraction,take the root of the numerator and denominator separately
−32536
Multiply by the Conjugate
325×3252−36×3252
Simplify
325×3252−36×535
Multiply the numbers
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Evaluate
−36×535
Multiply the terms
−330×5
Use the commutative property to reorder the terms
−5330
325×3252−5330
Multiply the numbers
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Evaluate
325×3252
The product of roots with the same index is equal to the root of the product
325×252
Calculate the product
3253
Transform the expression
356
Reduce the index of the radical and exponent with 3
52
52−5330
Reduce the fraction
More Steps

Evaluate
52−5
Use the product rule aman=an−m to simplify the expression
52−1−1
Subtract the terms
51−1
Simplify
5−1
5−330
Calculate
−5330
n=−5330
Alternative Form
n≈−0.621447
Show Solution
