Solve 3n^2+14n-5 - ScanMath

Question

Factor the expression

(n + 5) (3 n - 1)

Evaluate

3 n^{2} + 14 n - 5

Rewrite the expression

3 n^{2} + (- 1 + 15) n - 5

Calculate

3 n^{2} - n + 15 n - 5

Rewrite the expression

n \times 3 n - n + 5 \times 3 n - 5

Factor out n from the expression

n (3 n - 1) + 5 \times 3 n - 5

Factor out 5 from the expression

n (3 n - 1) + 5 (3 n - 1)

Solution

(n + 5) (3 n - 1)

Show Solution

n_{1} = - 5, n_{2} = \frac{1}{3}

Alternative Form

n_{1} = - 5, n_{2} = 0. \dot{3}

Evaluate

3 n^{2} + 14 n - 5

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

3 n^{2} + 14 n - 5 = 0

Factor the expression

More Steps

Evaluate

3 n^{2} + 14 n - 5

Rewrite the expression

3 n^{2} + (- 1 + 15) n - 5

Calculate

3 n^{2} - n + 15 n - 5

Rewrite the expression

n \times 3 n - n + 5 \times 3 n - 5

Factor out n from the expression

n (3 n - 1) + 5 \times 3 n - 5

Factor out 5 from the expression

n (3 n - 1) + 5 (3 n - 1)

Factor out 3 n - 1 from the expression

(n + 5) (3 n - 1)

(n + 5) (3 n - 1) = 0

When the product of factors equals 0,at least one factor is 0

n + 5 = 0 3 n - 1 = 0

Solve the equation for n

More Steps

Evaluate

n + 5 = 0

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

n = 0 - 5

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

n = - 5

n = - 5 3 n - 1 = 0

Solve the equation for n

More Steps

Evaluate

3 n - 1 = 0

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

3 n = 0 + 1

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

3 n = 1

Divide both sides

\frac{3 n}{3} = \frac{1}{3}

Divide the numbers

n = \frac{1}{3}

n = - 5 n = \frac{1}{3}

Solution

n_{1} = - 5, n_{2} = \frac{1}{3}

Alternative Form

n_{1} = - 5, n_{2} = 0. \dot{3}

Show Solution