Solve 4n^2+5n-636

Question

Factor the expression

(n - 12) (4 n + 53)

Evaluate

4 n^{2} + 5 n - 636

Rewrite the expression

4 n^{2} + (53 - 48) n - 636

Calculate

4 n^{2} + 53 n - 48 n - 636

Rewrite the expression

n \times 4 n + n \times 53 - 12 \times 4 n - 12 \times 53

Factor out n from the expression

n (4 n + 53) - 12 \times 4 n - 12 \times 53

Factor out - 12 from the expression

n (4 n + 53) - 12 (4 n + 53)

Solution

(n - 12) (4 n + 53)

Show Solution

n_{1} = - \frac{53}{4}, n_{2} = 12

Alternative Form

n_{1} = - 13.25, n_{2} = 12

Evaluate

4 n^{2} + 5 n - 636

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

4 n^{2} + 5 n - 636 = 0

Factor the expression

More Steps

Evaluate

4 n^{2} + 5 n - 636

Rewrite the expression

4 n^{2} + (53 - 48) n - 636

Calculate

4 n^{2} + 53 n - 48 n - 636

Rewrite the expression

n \times 4 n + n \times 53 - 12 \times 4 n - 12 \times 53

Factor out n from the expression

n (4 n + 53) - 12 \times 4 n - 12 \times 53

Factor out - 12 from the expression

n (4 n + 53) - 12 (4 n + 53)

Factor out 4 n + 53 from the expression

(n - 12) (4 n + 53)

(n - 12) (4 n + 53) = 0

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

n - 12 = 0 4 n + 53 = 0

Solve the equation for n

More Steps

Evaluate

n - 12 = 0

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

n = 0 + 12

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

n = 12

n = 12 4 n + 53 = 0

Solve the equation for n

More Steps

Evaluate

4 n + 53 = 0

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

4 n = 0 - 53

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

4 n = - 53

Divide both sides

\frac{4 n}{4} = \frac{- 53}{4}

Divide the numbers

n = \frac{- 53}{4}

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

n = - \frac{53}{4}

n = 12 n = - \frac{53}{4}

Solution

n_{1} = - \frac{53}{4}, n_{2} = 12

Alternative Form

n_{1} = - 13.25, n_{2} = 12

Show Solution