Solve 6n^221n-12 - ScanMath

Question

Simplify the expression

126 n^{3} - 12

Evaluate

6 n^{2} \times 21 n - 12

Solution

More Steps

Evaluate

6 n^{2} \times 21 n

Multiply the terms

126 n^{2} \times n

Multiply the terms with the same base by adding their exponents

126 n^{2 + 1}

Add the numbers

126 n^{3}

126 n^{3} - 12

Show Solution

Factor the expression

6 (21 n^{3} - 2)

Evaluate

6 n^{2} \times 21 n - 12

Multiply

More Steps

Evaluate

6 n^{2} \times 21 n

Multiply the terms

126 n^{2} \times n

Multiply the terms with the same base by adding their exponents

126 n^{2 + 1}

Add the numbers

126 n^{3}

126 n^{3} - 12

Solution

6 (21 n^{3} - 2)

Show Solution

Find the roots

n = \frac{3 882}{21}

Alternative Form

n \approx 0.456671

Evaluate

6 n^{2} \times 21 n - 12

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

6 n^{2} \times 21 n - 12 = 0

Multiply

More Steps

Multiply the terms

6 n^{2} \times 21 n

Multiply the terms

126 n^{2} \times n

Multiply the terms with the same base by adding their exponents

126 n^{2 + 1}

Add the numbers

126 n^{3}

126 n^{3} - 12 = 0

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

126 n^{3} = 0 + 12

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

126 n^{3} = 12

Divide both sides

\frac{126 n ^{3}}{126} = \frac{12}{126}

Divide the numbers

n^{3} = \frac{12}{126}

Cancel out the common factor 6

n^{3} = \frac{2}{21}

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

3 n^{3} = 3 \frac{2}{21}

Calculate

n = 3 \frac{2}{21}

Solution

More Steps

Evaluate

3 \frac{2}{21}

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

\frac{3 2}{3 21}

Multiply by the Conjugate

\frac{3 2 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{3 2 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3441

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

3 2 \times 441

Calculate the product

3882

\frac{3 882}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3 2 1^{2}

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

3 21 \times 2 1^{2}

Calculate the product

3 2 1^{3}

Reduce the index of the radical and exponent with 3

21

\frac{3 882}{21}

n = \frac{3 882}{21}

Alternative Form

n \approx 0.456671

Show Solution