Solve 2n^23n - 9 - ScanMath

Question

Simplify the expression

6 n^{3} - 9

Evaluate

2 n^{2} \times 3 n - 9

Solution

More Steps

Evaluate

2 n^{2} \times 3 n

Multiply the terms

6 n^{2} \times n

Multiply the terms with the same base by adding their exponents

6 n^{2 + 1}

Add the numbers

6 n^{3}

6 n^{3} - 9

Show Solution

Factor the expression

3 (2 n^{3} - 3)

Evaluate

2 n^{2} \times 3 n - 9

Multiply

More Steps

Evaluate

2 n^{2} \times 3 n

Multiply the terms

6 n^{2} \times n

Multiply the terms with the same base by adding their exponents

6 n^{2 + 1}

Add the numbers

6 n^{3}

6 n^{3} - 9

Solution

3 (2 n^{3} - 3)

Show Solution

Find the roots

n = \frac{3 12}{2}

Alternative Form

n \approx 1.144714

Evaluate

2 n^{2} \times 3 n - 9

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

2 n^{2} \times 3 n - 9 = 0

Multiply

More Steps

Multiply the terms

2 n^{2} \times 3 n

Multiply the terms

6 n^{2} \times n

Multiply the terms with the same base by adding their exponents

6 n^{2 + 1}

Add the numbers

6 n^{3}

6 n^{3} - 9 = 0

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

6 n^{3} = 0 + 9

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

6 n^{3} = 9

Divide both sides

\frac{6 n ^{3}}{6} = \frac{9}{6}

Divide the numbers

n^{3} = \frac{9}{6}

Cancel out the common factor 3

n^{3} = \frac{3}{2}

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

3 n^{3} = 3 \frac{3}{2}

Calculate

n = 3 \frac{3}{2}

Solution

More Steps

Evaluate

3 \frac{3}{2}

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

\frac{3 3}{3 2}

Multiply by the Conjugate

\frac{3 3 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

\frac{3 12}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 12}{2}

n = \frac{3 12}{2}

Alternative Form

n \approx 1.144714

Show Solution