Solve 6n^2 5n -4 - ScanMath

Question

Simplify the expression

30 n^{3} - 4

Evaluate

6 n^{2} \times 5 n - 4

Solution

More Steps

Evaluate

6 n^{2} \times 5 n

Multiply the terms

30 n^{2} \times n

Multiply the terms with the same base by adding their exponents

30 n^{2 + 1}

Add the numbers

30 n^{3}

30 n^{3} - 4

Show Solution

Factor the expression

2 (15 n^{3} - 2)

Evaluate

6 n^{2} \times 5 n - 4

Multiply

More Steps

Evaluate

6 n^{2} \times 5 n

Multiply the terms

30 n^{2} \times n

Multiply the terms with the same base by adding their exponents

30 n^{2 + 1}

Add the numbers

30 n^{3}

30 n^{3} - 4

Solution

2 (15 n^{3} - 2)

Show Solution

Find the roots

n = \frac{3 450}{15}

Alternative Form

n \approx 0.510873

Evaluate

6 n^{2} \times 5 n - 4

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

6 n^{2} \times 5 n - 4 = 0

Multiply

More Steps

Multiply the terms

6 n^{2} \times 5 n

Multiply the terms

30 n^{2} \times n

Multiply the terms with the same base by adding their exponents

30 n^{2 + 1}

Add the numbers

30 n^{3}

30 n^{3} - 4 = 0

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

30 n^{3} = 0 + 4

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

30 n^{3} = 4

Divide both sides

\frac{30 n ^{3}}{30} = \frac{4}{30}

Divide the numbers

n^{3} = \frac{4}{30}

Cancel out the common factor 2

n^{3} = \frac{2}{15}

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

3 n^{3} = 3 \frac{2}{15}

Calculate

n = 3 \frac{2}{15}

Solution

More Steps

Evaluate

3 \frac{2}{15}

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

\frac{3 2}{3 15}

Multiply by the Conjugate

\frac{3 2 \times 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 2 \times 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3225

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

3 2 \times 225

Calculate the product

3450

\frac{3 450}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3 1 5^{2}

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

3 15 \times 1 5^{2}

Calculate the product

3 1 5^{3}

Reduce the index of the radical and exponent with 3

15

\frac{3 450}{15}

n = \frac{3 450}{15}

Alternative Form

n \approx 0.510873

Show Solution