Solve 6n^2 13n-60

Question

Simplify the expression

78 n^{3} - 60

Evaluate

6 n^{2} \times 13 n - 60

Solution

More Steps

Evaluate

6 n^{2} \times 13 n

Multiply the terms

78 n^{2} \times n

Multiply the terms with the same base by adding their exponents

78 n^{2 + 1}

Add the numbers

78 n^{3}

78 n^{3} - 60

Show Solution

Factor the expression

6 (13 n^{3} - 10)

Evaluate

6 n^{2} \times 13 n - 60

Multiply

More Steps

Evaluate

6 n^{2} \times 13 n

Multiply the terms

78 n^{2} \times n

Multiply the terms with the same base by adding their exponents

78 n^{2 + 1}

Add the numbers

78 n^{3}

78 n^{3} - 60

Solution

6 (13 n^{3} - 10)

Show Solution

Find the roots

n = \frac{3 1690}{13}

Alternative Form

n \approx 0.91626

Evaluate

6 n^{2} \times 13 n - 60

To find the roots of the expression,set the expression equal to 0

6 n^{2} \times 13 n - 60 = 0

Multiply

More Steps

Multiply the terms

6 n^{2} \times 13 n

Multiply the terms

78 n^{2} \times n

Multiply the terms with the same base by adding their exponents

78 n^{2 + 1}

Add the numbers

78 n^{3}

78 n^{3} - 60 = 0

Move the constant to the right-hand side and change its sign

78 n^{3} = 0 + 60

Removing 0 doesn't change the value,so remove it from the expression

78 n^{3} = 60

Divide both sides

\frac{78 n ^{3}}{78} = \frac{60}{78}

Divide the numbers

n^{3} = \frac{60}{78}

Cancel out the common factor 6

n^{3} = \frac{10}{13}

Take the 3 -th root on both sides of the equation

3 n^{3} = 3 \frac{10}{13}

Calculate

n = 3 \frac{10}{13}

Solution

More Steps

Evaluate

3 \frac{10}{13}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 10}{3 13}

Multiply by the Conjugate

\frac{3 10 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Simplify

\frac{3 10 \times 3 169}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3169

The product of roots with the same index is equal to the root of the product

3 10 \times 169

Calculate the product

31690

\frac{3 1690}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3 1 3^{2}

The product of roots with the same index is equal to the root of the product

3 13 \times 1 3^{2}

Calculate the product

3 1 3^{3}

Reduce the index of the radical and exponent with 3

13

\frac{3 1690}{13}

n = \frac{3 1690}{13}

Alternative Form

n \approx 0.91626

Show Solution