Solve 3n^2-19n-1400

Question

Factor the expression

(n - 25) (3 n + 56)

Evaluate

3 n^{2} - 19 n - 1400

Rewrite the expression

3 n^{2} + (56 - 75) n - 1400

Calculate

3 n^{2} + 56 n - 75 n - 1400

Rewrite the expression

n \times 3 n + n \times 56 - 25 \times 3 n - 25 \times 56

Factor out n from the expression

n (3 n + 56) - 25 \times 3 n - 25 \times 56

Factor out - 25 from the expression

n (3 n + 56) - 25 (3 n + 56)

Solution

(n - 25) (3 n + 56)

Show Solution

n_{1} = - \frac{56}{3}, n_{2} = 25

Alternative Form

n_{1} = - 18. \dot{6}, n_{2} = 25

Evaluate

3 n^{2} - 19 n - 1400

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

3 n^{2} - 19 n - 1400 = 0

Factor the expression

More Steps

Evaluate

3 n^{2} - 19 n - 1400

Rewrite the expression

3 n^{2} + (56 - 75) n - 1400

Calculate

3 n^{2} + 56 n - 75 n - 1400

Rewrite the expression

n \times 3 n + n \times 56 - 25 \times 3 n - 25 \times 56

Factor out n from the expression

n (3 n + 56) - 25 \times 3 n - 25 \times 56

Factor out - 25 from the expression

n (3 n + 56) - 25 (3 n + 56)

Factor out 3 n + 56 from the expression

(n - 25) (3 n + 56)

(n - 25) (3 n + 56) = 0

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

n - 25 = 0 3 n + 56 = 0

Solve the equation for n

More Steps

Evaluate

n - 25 = 0

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

n = 0 + 25

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

n = 25

n = 25 3 n + 56 = 0

Solve the equation for n

More Steps

Evaluate

3 n + 56 = 0

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

3 n = 0 - 56

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

3 n = - 56

Divide both sides

\frac{3 n}{3} = \frac{- 56}{3}

Divide the numbers

n = \frac{- 56}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

n = - \frac{56}{3}

n = 25 n = - \frac{56}{3}

Solution

n_{1} = - \frac{56}{3}, n_{2} = 25

Alternative Form

n_{1} = - 18. \dot{6}, n_{2} = 25

Show Solution