Solve 9n^(3)-15n - ScanMath

Question

Factor the expression

3 n (3 n^{2} - 5)

Evaluate

9 n^{3} - 15 n

Rewrite the expression

3 n \times 3 n^{2} - 3 n \times 5

Solution

3 n (3 n^{2} - 5)

Show Solution

n_{1} = - \frac{15}{3}, n_{2} = 0, n_{3} = \frac{15}{3}

Alternative Form

n_{1} \approx - 1.290994, n_{2} = 0, n_{3} \approx 1.290994

Evaluate

9 n^{3} - 15 n

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

9 n^{3} - 15 n = 0

Factor the expression

3 n (3 n^{2} - 5) = 0

Divide both sides

n (3 n^{2} - 5) = 0

Separate the equation into 2 possible cases

n = 0 3 n^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

3 n^{2} - 5 = 0

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

3 n^{2} = 0 + 5

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

3 n^{2} = 5

Divide both sides

\frac{3 n ^{2}}{3} = \frac{5}{3}

Divide the numbers

n^{2} = \frac{5}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

n = \pm \frac{5}{3}

Simplify the expression

More Steps

Evaluate

\frac{5}{3}

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

\frac{5}{3}

Multiply by the Conjugate

\frac{5 \times 3}{3 \times 3}

Multiply the numbers

\frac{15}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{15}{3}

n = \pm \frac{15}{3}

Separate the equation into 2 possible cases

n = \frac{15}{3} n = - \frac{15}{3}

n = 0 n = \frac{15}{3} n = - \frac{15}{3}

Solution

n_{1} = - \frac{15}{3}, n_{2} = 0, n_{3} = \frac{15}{3}

Alternative Form

n_{1} \approx - 1.290994, n_{2} = 0, n_{3} \approx 1.290994

Show Solution