Solve 3(n^2)= 9(6-n)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - 6, n_{2} = 3

Evaluate

3 n^{2} = 9 (6 - n)

Expand the expression

More Steps

Evaluate

9 (6 - n)

Apply the distributive property

9 \times 6 - 9 n

Multiply the numbers

54 - 9 n

3 n^{2} = 54 - 9 n

Move the expression to the left side

3 n^{2} - 54 + 9 n = 0

Factor the expression

More Steps

Evaluate

3 n^{2} - 54 + 9 n

Evaluate

3 n^{2} + 9 n - 54

Rewrite the expression

3 n^{2} + 3 \times 3 n - 3 \times 18

Factor out 3 from the expression

3 (n^{2} + 3 n - 18)

Factor the expression

More Steps

Evaluate

n^{2} + 3 n - 18

Rewrite the expression

n^{2} + (6 - 3) n - 18

Calculate

n^{2} + 6 n - 3 n - 18

Rewrite the expression

n \times n + n \times 6 - 3 n - 3 \times 6

Factor out n from the expression

n (n + 6) - 3 n - 3 \times 6

Factor out - 3 from the expression

n (n + 6) - 3 (n + 6)

Factor out n + 6 from the expression

(n - 3) (n + 6)

3 (n - 3) (n + 6)

3 (n - 3) (n + 6) = 0

Divide the terms

(n - 3) (n + 6) = 0

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

n - 3 = 0 n + 6 = 0

Solve the equation for n

More Steps

Evaluate

n - 3 = 0

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

n = 0 + 3

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

n = 3

n = 3 n + 6 = 0

Solve the equation for n

More Steps

Evaluate

n + 6 = 0

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

n = 0 - 6

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

n = - 6

n = 3 n = - 6

Solution

n_{1} = - 6, n_{2} = 3

Show Solution