Solve 2(n^2)=n(n-3)/2

Evaluate

2 n^{2} = n \times \frac{n - 3}{2}

Multiply the terms

2 n^{2} = \frac{n ( n - 3 )}{2}

Multiply both sides of the equation by LCD

2 n^{2} \times 2 = \frac{n ( n - 3 )}{2} \times 2

Simplify the equation

4 n^{2} = \frac{n ( n - 3 )}{2} \times 2

Simplify the equation

More Steps

4 n^{2} = n^{2} - 3 n

Move the expression to the left side

3 n^{2} + 3 n = 0

Factor the expression

More Steps

3 n (n + 1) = 0

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

3 n = 0 n + 1 = 0

Solve the equation for n

n = 0 n + 1 = 0

Solve the equation for n

More Steps

n = 0 n = - 1

Solution

n_{1} = - 1, n_{2} = 0

Solve the quadratic equation