Solve ( 1/3 n^(2) 2n- 1/5 ) ( 1/4 n^(2)- 3/4 n-2) - ScanMath

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Type your math problem... ( 1/3 n^(2) 2n- 1/5 ) ( 1/4 n^(2)- 3/4 n-2)

Question

Simplify the expression

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{4}{3} n^{3} - \frac{1}{20} n^{2} + \frac{3}{20} n + \frac{2}{5}

Evaluate

(\frac{1}{3} n^{2} \times 2 n - \frac{1}{5}) (\frac{1}{4} n^{2} - \frac{3}{4} n - 2)

Multiply

More Steps

(\frac{2}{3} n^{3} - \frac{1}{5}) (\frac{1}{4} n^{2} - \frac{3}{4} n - 2)

Apply the distributive property

\frac{2}{3} n^{3} \times \frac{1}{4} n^{2} - \frac{2}{3} n^{3} \times \frac{3}{4} n - \frac{2}{3} n^{3} \times 2 - \frac{1}{5} \times \frac{1}{4} n^{2} - (- \frac{1}{5} \times \frac{3}{4} n) - (- \frac{1}{5} \times 2)

Multiply the terms

More Steps

\frac{1}{6} n^{5} - \frac{2}{3} n^{3} \times \frac{3}{4} n - \frac{2}{3} n^{3} \times 2 - \frac{1}{5} \times \frac{1}{4} n^{2} - (- \frac{1}{5} \times \frac{3}{4} n) - (- \frac{1}{5} \times 2)

Multiply the terms

More Steps

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{2}{3} n^{3} \times 2 - \frac{1}{5} \times \frac{1}{4} n^{2} - (- \frac{1}{5} \times \frac{3}{4} n) - (- \frac{1}{5} \times 2)

Multiply the numbers

More Steps

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{4}{3} n^{3} - \frac{1}{5} \times \frac{1}{4} n^{2} - (- \frac{1}{5} \times \frac{3}{4} n) - (- \frac{1}{5} \times 2)

Multiply the numbers

More Steps

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{4}{3} n^{3} - \frac{1}{20} n^{2} - (- \frac{1}{5} \times \frac{3}{4} n) - (- \frac{1}{5} \times 2)

Multiply the numbers

More Steps

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{4}{3} n^{3} - \frac{1}{20} n^{2} - (- \frac{3}{20} n) - (- \frac{1}{5} \times 2)

Multiply the numbers

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{4}{3} n^{3} - \frac{1}{20} n^{2} - (- \frac{3}{20} n) - (- \frac{2}{5})

Solution

\frac{1}{6} n^{5} - \frac{1}{2} n^{4} - \frac{4}{3} n^{3} - \frac{1}{20} n^{2} + \frac{3}{20} n + \frac{2}{5}

Show Solution

Factor the expression

\frac{1}{60} (10 n^{3} - 3) (n^{2} - 3 n - 8)

Show Solution

Find the roots

n_{1} = \frac{3 - 41}{2}, n_{2} = \frac{3 300}{10}, n_{3} = \frac{3 + 41}{2}

Alternative Form

n_{1} \approx - 1.701562, n_{2} \approx 0.669433, n_{3} \approx 4.701562

Evaluate

(\frac{1}{3} n^{2} \times 2 n - \frac{1}{5}) (\frac{1}{4} n^{2} - \frac{3}{4} n - 2)

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

(\frac{1}{3} n^{2} \times 2 n - \frac{1}{5}) (\frac{1}{4} n^{2} - \frac{3}{4} n - 2) = 0

Multiply

More Steps

(\frac{2}{3} n^{3} - \frac{1}{5}) (\frac{1}{4} n^{2} - \frac{3}{4} n - 2) = 0

Separate the equation into 2 possible cases

\frac{2}{3} n^{3} - \frac{1}{5} = 0 \frac{1}{4} n^{2} - \frac{3}{4} n - 2 = 0

Solve the equation

More Steps

n = \frac{3 300}{10} \frac{1}{4} n^{2} - \frac{3}{4} n - 2 = 0

Solve the equation

More Steps

n = \frac{3 300}{10} n = \frac{3 + 41}{2} n = \frac{3 - 41}{2}

Solution

n_{1} = \frac{3 - 41}{2}, n_{2} = \frac{3 300}{10}, n_{3} = \frac{3 + 41}{2}

Alternative Form

n_{1} \approx - 1.701562, n_{2} \approx 0.669433, n_{3} \approx 4.701562

Show Solution