Solve 6n^(2)-36n-240=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - 4, n_{2} = 10

Evaluate

6 n^{2} - 36 n - 240 = 0

Factor the expression

More Steps

Evaluate

6 n^{2} - 36 n - 240

Rewrite the expression

6 n^{2} - 6 \times 6 n - 6 \times 40

Factor out 6 from the expression

6 (n^{2} - 6 n - 40)

Factor the expression

More Steps

Evaluate

n^{2} - 6 n - 40

Rewrite the expression

n^{2} + (4 - 10) n - 40

Calculate

n^{2} + 4 n - 10 n - 40

Rewrite the expression

n \times n + n \times 4 - 10 n - 10 \times 4

Factor out n from the expression

n (n + 4) - 10 n - 10 \times 4

Factor out - 10 from the expression

n (n + 4) - 10 (n + 4)

Factor out n + 4 from the expression

(n - 10) (n + 4)

6 (n - 10) (n + 4)

6 (n - 10) (n + 4) = 0

Divide the terms

(n - 10) (n + 4) = 0

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

n - 10 = 0 n + 4 = 0

Solve the equation for n

More Steps

Evaluate

n - 10 = 0

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

n = 0 + 10

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

n = 10

n = 10 n + 4 = 0

Solve the equation for n

More Steps

Evaluate

n + 4 = 0

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

n = 0 - 4

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

n = - 4

n = 10 n = - 4

Solution

n_{1} = - 4, n_{2} = 10

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