Solve 30(n-30)=n(n-70)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = 10, n_{2} = 90

Evaluate

30 (n - 30) = n (n - 70)

Swap the sides

n (n - 70) = 30 (n - 30)

Expand the expression

More Steps

Evaluate

n (n - 70)

Apply the distributive property

n \times n - n \times 70

Multiply the terms

n^{2} - n \times 70

Use the commutative property to reorder the terms

n^{2} - 70 n

n^{2} - 70 n = 30 (n - 30)

Expand the expression

More Steps

Evaluate

30 (n - 30)

Apply the distributive property

30 n - 30 \times 30

Multiply the numbers

30 n - 900

n^{2} - 70 n = 30 n - 900

Move the expression to the left side

n^{2} - 100 n + 900 = 0

Factor the expression

More Steps

Evaluate

n^{2} - 100 n + 900

Rewrite the expression

n^{2} + (- 10 - 90) n + 900

Calculate

n^{2} - 10 n - 90 n + 900

Rewrite the expression

n \times n - n \times 10 - 90 n + 90 \times 10

Factor out n from the expression

n (n - 10) - 90 n + 90 \times 10

Factor out - 90 from the expression

n (n - 10) - 90 (n - 10)

Factor out n - 10 from the expression

(n - 90) (n - 10)

(n - 90) (n - 10) = 0

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

n - 90 = 0 n - 10 = 0

Solve the equation for n

More Steps

Evaluate

n - 90 = 0

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

n = 0 + 90

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

n = 90

n = 90 n - 10 = 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 = 90 n = 10

Solution

n_{1} = 10, n_{2} = 90

Show Solution